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ΔABC cân tại A\(\Rightarrow AB=AC\Rightarrow\dfrac{1}{2}AB=\dfrac{1}{2}AC\Rightarrow AN=NB=AM=MC\)
Xét ΔAMB và Δ ANC có:
\(AM=AN\left(cmt\right)\)
Chung \(\widehat{A}\)
\(AB=AC\left(cmt\right)\)
⇒ΔAMB = Δ ANC (c.g.c)
⇒ BM = CN (2 cạnh tương ứng)
ta có: BN = CM ( ABC cân, BM và CN là trung tuyến )
Xét tam giác BMC và tam giác CNB, có:
CN = CM ( cmt )
góc B = góc C ( ABC cân )
BC: cạnh chung
Vậy tam giác BMC = tam giác CNB ( c.g.c )
=> BM = CN ( 2 cạnh tương ứng )
c,2x2+(−6)3:27=0c,2x2+(-6)3:27=0
⇒2x2+(−216):27=0⇒2x2+(-216):27=0
⇒2x2+(−8)=0⇒2x2+(-8)=0
⇒2x2=0−(−8)⇒2x2=0-(-8)
⇒2x2=8⇒2x2=8
⇒x2=8:2⇒x2=8:2
⇒x2=4⇒x2=4
⇒{x2=22x2=(−2)2⇒{x2=22x2=(-2)2
⇒{x=2x=−2⇒{x=2x=-2
Vậy x∈{(−2);2}
\(\frac{x+1}{2009}+\frac{x+2}{2008}+\frac{x+3}{2007}=\frac{x+10}{2000}+\frac{x+11}{1999}+\frac{x+12}{1998}.\)
\(\frac{x+1}{2009}+1+\frac{x+2}{2008}+1+\frac{x+3}{2007}+1=\frac{x+10}{2000}+1+\frac{x+11}{1999}+1+\frac{x+12}{1998}+1.\)(cộng 2 vế cho 3)
\(\frac{x+1}{2009}+\frac{2009}{2009}+\frac{x+2}{2008}+\frac{2008}{2008}+\frac{x+3}{2007}+\frac{2007}{2007}=\frac{x+10}{2000}+\frac{2000}{2000}+\frac{x+11}{1999}+\frac{1999}{1999}+\frac{x+12}{1998}+\frac{1998}{1998}.\)
\(\frac{x+2010}{2009}+\frac{x+2010}{2008}+\frac{x+2010}{2007}=\frac{x+2010}{2000}+\frac{x+2010}{1999}+\frac{x+2010}{1998}.\)
\(\frac{x+2010}{2009}+\frac{x+2010}{2008}+\frac{x+2010}{2007}-\frac{x+2010}{2000}-\frac{x+2010}{1999}-\frac{x+2010}{1998}=0\)
x+2010=0
x=-2010
\(\frac{x+1}{2009}+\frac{x+2}{2008}+\frac{x+3}{2007}=\frac{x+10}{2000}+\frac{x+11}{1999}+\frac{x+12}{1998}\)
\(\Leftrightarrow\left(1+\frac{x+1}{2009}\right)+\left(1+\frac{x+2}{2008}\right)+\left(1+\frac{x+3}{2007}\right)\)
\(=\left(1+\frac{x+10}{2000}\right)+\left(1+\frac{x+11}{1999}\right)+\left(1+\frac{x+12}{1998}\right)\)
\(\Leftrightarrow\frac{x+2010}{2009}+\frac{x+2010}{2008}+\frac{x+2010}{2007}=\frac{x+2010}{2000}+\frac{x+2010}{1999}+\frac{x=2010}{1998}\)
\(\Leftrightarrow\frac{x+2010}{2009}+\frac{x+2010}{2008}+\frac{x+2010}{2007}-\frac{x+2010}{2000}-\frac{x+2010}{1999}-\frac{x+2010}{1998}\)
\(=0\)
\(\Leftrightarrow\left(x+2010\right)\left(\frac{1}{2009}+\frac{1}{2008}+\frac{1}{2007}-\frac{1}{2000}-\frac{1}{1999}-\frac{1}{1998}\right)=0\)
\(\Leftrightarrow x+2010=0\)
\(\Leftrightarrow x=-2010\)
Ta có:
-7/13=-70/130=-7.10/13.10
-4/13=-40/130=-4.10/13.10
=>p/s đó là a.13/10.13
=>-7.10<a.13<-4.10
=>a=-4;-5
Vậy p/s đó là:-4/10 và -5/10
(x - 1)x + 2 = (x - 1)x + 6
(x - 1)x + 2 - (x - 1)x + 6 = 0
(x - 1)x + 2.[1 - (x - 1)x + 4] = 0
\(\Rightarrow\) (x - 1)x + 2 = 0 hoặc 1 - (x - 1)x + 4 = 0
\(\Rightarrow\) x - 1 = 0 hoặc (x - 1)x + 4 = 1
\(\Rightarrow\) x = 1 hoặc x - 1 = 1 hoặc x - 1 = - 1
\(\Rightarrow\) x = 1 hoặc x = 2 hoặc x = 0
Vậy \(x\in\left\{0;1;2\right\}\)
| x - 3y - 1 | + | y - 4 | = 0
mà GTTĐ luôn lớn hơn hoặc bằng 0
=> y - 4 = 0 và x - 3y - 1 = 0
=> y = 4
=> x - 12 - 1 = 0
x - 13 = 0
x = 13
Vậy, x = 13, y = 4
Học tốt nhé :))
Bài 1: Tính hợp lí:
\(a)\)\(\frac{14}{57}+\frac{29}{23}-\frac{71}{57}+\frac{-6}{23}\)
\(=\)\(\left(\frac{14}{57}-\frac{71}{57}\right)+\left(\frac{29}{23}+\frac{-6}{23}\right)\)
\(=\)\(\left(-\frac{57}{57}\right)+\left(\frac{23}{23}\right)\)
\(=\)\(\left(-1\right)+1\)
\(=\)\(0\)
\(b)\)\(\frac{5}{12}.\left(\frac{-3}{4}\right)+\frac{7}{12}.\left(\frac{-3}{4}\right)\)
\(=\)\(\left(\frac{-3}{4}\right).\left(\frac{5}{12}+\frac{7}{12}\right)\)
\(=\)\(\left(\frac{-3}{4}\right).1\)
\(=\)\(-\frac{3}{4}\)
\(c)\)\(\left(\frac{-3}{11}\div\frac{5}{22}\right).\left(\frac{-15}{3}\div\frac{26}{3}\right)\)
\(=\)\(\left(\frac{-3}{11}.\frac{22}{5}\right).\left(\frac{-15}{3}.\frac{3}{26}\right)\)
\(=\)\(\frac{-6}{5}.\frac{-15}{26}\)
\(=\)\(\frac{9}{13}\)
\(d)\)\(\left(0,25\right)^{100}.4^{103}\)
\(=\)\(\left(\frac{1}{4}\right)^{100}.4^{103}\)
\(=\)\(\left(\frac{1}{4}.4\right)^{100+103}\)
\(=\)\(1^{203}\)
\(=\)\(1\)
Bài 2: Tìm x, biết:
\(a)\)\(\left(\frac{3}{7}-2x\right)^2=\frac{4}{9}\)
\(\Leftrightarrow\)\(\left(\frac{3}{7}-2x\right)^2=\left(\frac{2}{3}\right)^2\)
\(\Leftrightarrow\)\(\frac{3}{7}-2x=\frac{2}{3}\)
\(\Leftrightarrow\)\(2x=\frac{3}{7}-\frac{2}{3}\)
\(\Leftrightarrow\)\(2x=\frac{-5}{21}\)
\(\Leftrightarrow\)\(x=\frac{-5}{21}\div2\)
\(\Leftrightarrow\)\(x=\frac{-5}{42}\)
\(b)\)\(x+5,5=7,5\)
\(\Leftrightarrow\)\(x=7,5-5,5\)
\(\Leftrightarrow\)\(x=2\)