Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Bài 5: GTNN chứ nhỉ?
Với mọi gt của \(x;y\in R\) ta có:
\(x^2+3\left|y-2\right|+1\ge1\)
Hay \(A\ge1\) với mọi gt của \(x;y\in R\)
Dấu "=" sảy ra khi và chỉ khi \(\left\{{}\begin{matrix}x=0\\y=2\end{matrix}\right.\)
Vậy..................
Bài 6: GTLN chứ?
Với mọi giá trị của \(x\in R\) ta có:
\(-\left(2x-1\right)^2\le0\Rightarrow-5-\left(2x-1\right)^2\le-5\)
Hay \(B\le5\) với mọi giá trị của \(x\in R\)
Dấu "=" sảy ra khi và chỉ khi \(x=\dfrac{1}{2}\)
Vậy...................
Bài 4 :
\(a,3^{15}-9^6=3^{15}-\left(3^2\right)^6=3^{15}-3^{12}=3^{12}\left(3^3-1\right)=3^{12}.26=3^{12}.2.13⋮\left(đpcm\right)\)
\(b,8^7-2^{18}=\left(2^3\right)^7-2^{18}=2^{21}-2^{18}=2^{18}\left(2^3-1\right)=2^{18}.7=2^{17}.2.7=2^{17}.14⋮14\left(đpcm\right)\)
Bài 5 :
\(A=1^2+3^2+6^2+9^2+.............+39^2\)
\(=1+3^2+\left(6^2+9^2+.........+39^2\right)\)
\(=10+3^2\left(2^2+3^2+.........+13^2\right)\)
\(=10+3^2.818\)
\(=10+9.818\)
\(=7372\)
Ta có
• A=1+34+38+312
=>34.A=34+38+312+316
<=>81.A-A=316-1
<=>A=(316-1)/80=538084
•B=1+32+34+36+38+310+312+314
=>32.B=32+34+36+38+310+312+314+316
<=>8.B=316-1
<=>B=(316-1)/8=53808400
Vậy Q=A/B=538084/53808400=1/100=0.01
\(\frac{4^{10}+8^4}{4^5+8^6}=\frac{\left(2^2\right)^{10}+\left(2^3\right)^4}{\left(2^2\right)^5+\left(2^3\right)^6}=\frac{2^{2.10}+2^{3.4}}{2^{2.5}+2^{3.6}}=\)
\(=\frac{2^{20}+2^{12}}{2^{10}+2^{18}}\)
Lời giải:
\(\frac{1+3^4+3^8+3^{12}}{1+3^2+3^4+3^6+3^8+3^{10}+3^{12}+3^{14}}=\frac{1+3^4+3^8+3^{12}}{(1+3^4+3^8+3^{12})+(3^2+3^6+3^{10}+3^{14})}\)
\(=\frac{1+3^4+3^8+3^{12}}{(1+3^4+3^8+3^{12})+3^2(1+3^4+3^{8}+3^{12})}\)
\(=\frac{1+3^4+3^8+3^{12}}{(1+3^2)(1+3^4+3^8+3^{12})}=\frac{1}{1+3^2}=\frac{1}{10}\)
Lời giải:
\(\frac{1+3^4+3^8+3^{12}}{1+3^2+3^4+3^6+3^8+3^{10}+3^{12}+3^{14}}=\frac{1+3^4+3^8+3^{12}}{(1+3^4+3^8+3^{12})+(3^2+3^6+3^{10}+3^{14})}\)
\(=\frac{1+3^4+3^8+3^{12}}{(1+3^4+3^8+3^{12})+3^2(1+3^4+3^{8}+3^{12})}\)
\(=\frac{1+3^4+3^8+3^{12}}{(1+3^2)(1+3^4+3^8+3^{12})}=\frac{1}{1+3^2}=\frac{1}{10}\)
a) Ta có: \(\dfrac{-5}{7}\left(\dfrac{14}{5}-\dfrac{7}{10}\right):\left|-\dfrac{2}{3}\right|-\dfrac{3}{4}\left(\dfrac{8}{9}+\dfrac{16}{3}\right)+\dfrac{10}{3}\left(\dfrac{1}{3}+\dfrac{1}{5}\right)\)
\(=\dfrac{-5}{7}\cdot\dfrac{3}{2}\cdot\dfrac{21}{10}-\dfrac{3}{4}\cdot\dfrac{56}{3}+\dfrac{10}{3}\cdot\dfrac{8}{15}\)
\(=\dfrac{-9}{4}-14+\dfrac{16}{9}\)
\(=\dfrac{-1621}{126}\)
b) Ta có: \(\dfrac{17}{-26}\cdot\left(\dfrac{1}{6}-\dfrac{5}{3}\right):\dfrac{17}{13}-\dfrac{20}{3}\left(\dfrac{2}{5}-\dfrac{1}{4}\right)+\dfrac{2}{3}\left(\dfrac{6}{5}-\dfrac{9}{2}\right)\)
\(=\dfrac{-17}{26}\cdot\dfrac{13}{17}\cdot\dfrac{-3}{2}-\dfrac{20}{3}\cdot\dfrac{3}{20}+\dfrac{2}{3}\cdot\dfrac{-33}{10}\)
\(=\dfrac{3}{4}-1-\dfrac{11}{5}\)
\(=-\dfrac{49}{20}\)
\(A=\dfrac{4^{10}+8^4}{4^5+8^6}\)
\(A=\dfrac{2^{20}+2^{12}}{2^{10}+2^{18}}=\dfrac{\left(2^8+1\right).2^{12}}{\left(1+2^8\right).2^{10}}\)
\(=\dfrac{\left(256+1\right).2^2}{1+256}=\dfrac{257.2^2}{257}=2^2\)
\(B=\dfrac{1+3^4+3^8+3^{12}}{1+3^2+3^4+3^6+3^8+3^{10}+3^{12}+3^{14}}\)
\(=\dfrac{1+81+6561+3^{12}}{1+9+81+729+6561+59049+3^{12}+3^{14}}\)
\(=\dfrac{6643+3^{12}}{91+719+6561+59049+3^{12}+3^{14}}\)
\(=\dfrac{6643+3^{12}}{66430+3^{12}+3^{14}}\)
P/s : Nổi hứng lên thì lm chứ k bt đúng hay sai :V
B sai bae nhs