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1. a) Ta có: M = |x + 15/19| \(\ge\)0 \(\forall\)x
Dấu "=" xảy ra <=> x + 15/19 = 0 <=> x = -15/19
Vậy MinM = 0 <=> x = -15/19
b) Ta có: N = |x - 4/7| - 1/2 \(\ge\)-1/2 \(\forall\)x
Dấu "=" xảy ra <=> x - 4/7 = 0 <=> x = 4/7
Vậy MinN = -1/2 <=> x = 4/7
2a) Ta có: P = -|5/3 - x| \(\le\)0 \(\forall\)x
Dấu "=" xảy ra <=> 5/3 - x = 0 <=> x = 5/3
Vậy MaxP = 0 <=> x = 5/3
b) Ta có: Q = 9 - |x - 1/10| \(\le\)9 \(\forall\)x
Dấu "=" xảy ra <=> x - 1/10 = 0 <=> x = 1/10
Vậy MaxQ = 9 <=> x = 1/10
Bài 2:
1)
a) \(\frac{3}{5}-x=25\%\)
=> \(\frac{3}{5}-x=\frac{1}{4}\)
=> \(x=\frac{3}{5}-\frac{1}{4}\)
=> \(x=\frac{7}{20}\)
Vậy \(x=\frac{7}{20}.\)
b) \(0,16:x=x:36\)
=> \(\frac{0,16}{x}=\frac{x}{36}\)
=> \(0,16.36=x.x\)
=> \(x.x=\frac{144}{25}\)
=> \(x^2=\frac{144}{25}\)
=> \(\left[{}\begin{matrix}x=\frac{12}{5}\\x=-\frac{12}{5}\end{matrix}\right.\)
Vậy \(x\in\left\{\frac{12}{5};-\frac{12}{5}\right\}.\)
2)
a) Ta có: \(5x=7y.\)
=> \(\frac{x}{y}=\frac{7}{5}\)
=> \(\frac{x}{7}=\frac{y}{5}\) và \(y-x=18.\)
Áp dụng tính chất dãy tỉ số bằng nhau ta được:
\(\frac{x}{7}=\frac{y}{5}=\frac{y-x}{5-7}=\frac{18}{-2}=-9.\)
\(\left\{{}\begin{matrix}\frac{x}{7}=-9=>x=\left(-9\right).7=-63\\\frac{y}{5}=-9=>y=\left(-9\right).5=-45\end{matrix}\right.\)
Vậy \(\left(x;y\right)=\left(-63;-45\right).\)
b) Ta có: \(\frac{x}{y}=0,8.\)
=> \(\frac{x}{y}=\frac{4}{5}\)
=> \(\frac{x}{4}=\frac{y}{5}\) và \(x+y=18.\)
Áp dụng tính chất dãy tỉ số bằng nhau ta được:
\(\frac{x}{4}=\frac{y}{5}=\frac{x+y}{4+5}=\frac{18}{9}=2.\)
\(\left\{{}\begin{matrix}\frac{x}{4}=2=>x=2.4=8\\\frac{y}{5}=2=>y=2.5=10\end{matrix}\right.\)
Vậy \(\left(x;y\right)=\left(8;10\right).\)
Mình chỉ làm thế này thôi nhé.
Chúc bạn học tốt!
\(\frac{4}{5}x+0=4,5\)
\(\frac{4}{5}x=4,5\)
\(x=4,5:\frac{4}{5}\)
\(x=5,625\)
vậy \(x=5,625\)
\(\frac{x}{3}=\frac{-5}{9}\)
\(\Rightarrow9x=-5.3\)
\(\Rightarrow9x=-15\)
\(\Rightarrow x=\frac{-5}{3}\)
vậy \(x=\frac{-5}{3}\)
\(\left|x+5\right|-\frac{1}{3}=\frac{2}{3}\)
\(\left|x+5\right|=\frac{2}{3}+\frac{1}{3}\)
\(\left|x+5\right|=1\)
\(\Rightarrow\orbr{\begin{cases}x+5=1\\x+5=-1\end{cases}}\Rightarrow\orbr{\begin{cases}x=-4\\x=-6\end{cases}}\)
vậy \(\orbr{\begin{cases}x=-4\\x=-6\end{cases}}\)
\(\left(x-2\right)^3=-125\)
\(\left(x-2\right)^3=\left(-5\right)^3\)
\(\Rightarrow x-2=-5\)
\(\Rightarrow x=-3\)
vậy \(x=-3\)
Bài 1 :\(a,=\frac{4}{1.3}.\frac{9}{2.4}.\frac{16}{3.5}...\frac{100^2}{99.101}\)
\(=\frac{2.3.4...100}{1.2.3...99}.\frac{2.3.4...100}{3.4...101}\)
\(=100.\frac{2}{101}=\frac{200}{101}\)
#)Giải :
a) \(\left(5x+1\right)^2=\frac{36}{49}\Leftrightarrow\left(5x+1\right)^2=\left(\frac{6}{7}\right)^2\Leftrightarrow5x+1=\frac{6}{7}\Leftrightarrow5x=-\frac{1}{7}\Leftrightarrow x=-\frac{1}{35}\)
b) \(\left(x-\frac{2}{9}\right)^3=\left(\frac{2}{3}\right)^6\Leftrightarrow\left(x-\frac{2}{9}\right)^3=\left[\left(\frac{2}{3}\right)^2\right]^3\Leftrightarrow x-\frac{2}{9}=\left(\frac{2}{3}\right)^2=\frac{4}{9}\Leftrightarrow x=\frac{2}{3}\)
c) \(\left(8x-1\right)^{2x+1}=5^{2x+1}\Leftrightarrow8x-1=5\Leftrightarrow8x=6\Leftrightarrow x=\frac{6}{8}\)
a) \(\left(5x+1\right)^2=\frac{36}{49}\)
\(\left(5x+1\right)^2=\frac{6^2}{7^2}\)
\(\left(5x+1\right)^2=\left(\frac{6}{7}\right)^2\)
\(\Leftrightarrow5x+1=\frac{6}{7}\)
\(5x=\frac{6}{7}-1\)
\(5x=\frac{6}{7}-\frac{7}{7}\)
\(5x=-\frac{1}{7}\)
\(x=-\frac{1}{7}\div5\)
\(x=-\frac{1}{7}\times\frac{1}{5}\)
\(x=-\frac{1}{35}\)
Vậy \(x=-\frac{1}{35}\)
1
\(\frac{x-3}{4}=\frac{y+5}{3}=\frac{z-4}{5}=\frac{2x-6}{8}=\frac{3y+15}{9}=\frac{4z-16}{20}\)
\(=\frac{2x+3y-4z-6+15+16}{-3}=-\frac{100}{3}\)
Làm nốt
2
\(\left|x-2\right|\ge0\) dấu "=" xảy ra tại x=2
\(\left(x-y\right)^2\ge0\) dấu "=" xảy ra tại x=y
\(3\sqrt{z^2+9}\ge3\sqrt{9}=9\) dấu "=" xảy ra tại z=0
\(\Rightarrow C\ge0+0+9+16=25\) dấu "=" xảy ra tại x=y=2;z=0
5
Chứng minh \(1< M< 2\) là OK
a,thay x=1,y=-1
=>A=(15.1+2.-1)-[(2.1+3)-(5.1+-1)]=13-[5-4]=12
b,thay=-1/2,y=1/7
=>B=4
1) \(\left(9^9\right)^{2013}\)= 10269363159364666440076552322773341581561034085240554413684171629845226550910869063141084455165024846467308031862801839537350602585807388907790165677831287422774432660306450530003706882130019126660033621304145739244276173577048090504994820917529469442173652905242934472777858750567472632994664600381934224746675284242716804187707473971153049296389564538282393321100521850729158342672916978486633073346395087524709304026115423816203365757494638423131935882476286148041225377521573071731453557120367321995775004742604569764745022389412766013722532450077367619939069300519001702898185102392773927389960480888542356324726363237536898205586978830302184325193226223435916070961038034935786871565694168032483034776261863802471075705726878653433383001001189241926035182758070542398573188268383074169109020402590360496218759242201271963792394715618265594345634230758007244699004003000401590521959773595723533039737036430015710879179131370760647094133072554170794993632842471406497462695365166916803272574522454401382663974485565680530010978750425197889269057395033275863668478654934441334494555064318484689342316306971521024595876939555467943409513599739742465719710957307401039466505018857934554613930415045936664298639272058657312601916520149572941057253546060280658091085857108287350235860520376248626158812551702239866122771402598673086936929135243309297996461647086887656015121093133495745098227813854645587494331845951709269358587499740880686161437051001446721645931603701931366046756571915591346082194099535179864942435147889719664866893951993209328180552969033445416386172074158156509068184846110009877655498411796133585929465285105476632644661698885141470189436283199349798153583068536942505793691702852246620602269418445330834508954131444268765759312479343419904740139320879242064290138393396190814854006875023217633358501559386869629903562803482598907058580834642187008732774069291138122707731009317247214463199502007349382592744206845610622073119291353793177956259701743316926165329688122906721927196323010889181055169806499566546884164914042278508330036064549558133226697031247070510887763306579421433675607558954912396327853467424003335216349883637063258300867587330031070320552690888583962060709425761455244473416175295550790206629899652326841562128125494362697380378913996157037213809010909152617053065047965873644302701915161491422477028822914991812751244014648364815652852259663562101505343929698300364745277267393347355428142967482152321747112276920645950373078036691708170463157769001081433039723940115958277368318945023698370418990114114623681030598771547893253242183396733689941466450154464716467140441700170890131070394317235669249736167939422225531914712053400394591025170046527933941931808727717700810490226657457458014925192262802223793377911267650955266657089009585212112836905894381397018270698103556284576894624491741924724548232777077039317695115234021720883233465113399660643038825392305224594945823567653088326327442095353311628349624602121813895038502370886964075117719039885809760171422727129924473839457315768243597403319870636550055160900303769922718752206531201831705424385675834623470898120798414884603237556758496483422249797988913495971144948857810070808962140027449957839158509072309335228612816014153586809180977765327121627937134049967684345369108329599698221680897904237253646696104638289317058937956786704502654705018578331925049052381574371364079244827076900746007044670044607514934428774185406569688113571812978834960339563464520445275203854387799426090303262175550913985879685323013395273140584906121284898600419987993686188204435391094252218471390818917130390872182868519308994839897218982949442429019573247952912905380490755419913598457819276169417786284482347581370093174347981877489100149059409603635202204843390807300768332120719828797936653584404544694348383212549192087418173867785361221768506688864308755986946608953282003111974359205430482715512293489410742551889057944409965962731729135907369164794520884407474498460942159861999051690799986820439014933471232036918567390365835132305185662258913590669721711271035876498544692676850173083777815138713451735852959497582505542139720996338872994246201493700854225531805769779199297405335600737006903257207290820931044945024227595231128387120276064384227546402934361068266072587525725727012002788329077620146531366428926553058456985976818503072684025934586637898483958234508662818031180715524520776171094013494021013676728110150423914944710134238003487063081238423668330925015539056597900840885380931769197169725833541445689013104266424340197869967258623982371657927554051872347209361532830788078019771804179098819400418948649540270834597079029891053990824778600110747558315677420029212621805618132160031130257415664172691492945292697559304231368145501988941653172710920650443181254274948908249495935867675652007874393961066550920282780133604505587836446569409476792952876000047659924818891904298270222076421357886611744774356481805662861913303332953231470607411006298630956870297224099368538952834326914631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1)
a) Theo đề ta có:
(99)2013 = 99.2013= 918117
Ta có:
91 = 9 có chữ số tận cùng là 9
92 = 81 có chữ số tận cùng là 1
và 918117 = 92.9058. 9 = (92)9058 .9 ( mình giải thích thêm là mình nhân 9 để cùng cơ số và cộng các tử lại là 2.9058 + 1 = 18117)
Vì 92 có chữ số tận cùng là 1
Nên (92)9058 cũng có chữ số tận cùng là 1
\(\Rightarrow\)918117 = (...1) .9
\(\Rightarrow\)918117 = (...9)
Vậy chữ số tận cùng của (99)2013 là 9
b) Ta có:
20081 = 2008 có chữ số tận cùng là 8
20082 = (...4) có chữ số tận cùng là 4 (vì 8.8=64)
20083 = (...2) có chữ số tận cùng là 2 (vì 4.8=32)
20084 = (...6) có chữ số tận cùng là 6 (vì 2.8=16)
và 2008100 = 20084.25= (20084)25
Vì 20084 có chữ số tận cùng là 6
Nên (20084)25 cũng có chữ số tận cùng là 6
Vậy 2008100 có chữ số tận cùng là 6