giúp mình vớiiii

\(\Leftrightarrow12a^2-4b^2=3a^2+3b^2\)

\(\Leftrightarrow9a^2=7b^2\)

\(\Leftrightarrow\dfrac{a^2}{b^2}=\dfrac{7}{9}\)

hay \(\dfrac{a}{b}\in\left\{\dfrac{\sqrt{7}}{3};-\dfrac{\sqrt{7}}{3}\right\}\)

\(\dfrac{3a^2-b^2}{a^2+b^2}=\dfrac{3}{4}\)

\(\Leftrightarrow4.\left(3a^2-b^2\right)=3\left(a^2+b^2\right)\)

\(\Leftrightarrow12a^2-4b^2=3a^2+3b^2\)

\(\Leftrightarrow12a^2-3a^2=3b^2+4b^2\)

\(\Leftrightarrow9a^2=7b^2\)

\(\Leftrightarrow\dfrac{a^2}{b^2}=\dfrac{7}{9}\)

\(\text{hoặc }\dfrac{a}{b}=\pm\dfrac{\sqrt{7}}{3}\)

Ta có công thức tổng quát như sau:

\(A=n^k+n^{k+1}+n^{k+2}+...+n^{k+x}\Rightarrow A=\dfrac{n^{k+x+1}-n^k}{n-1}\)

Áp dụng ta có:

\(A=1+4+4^2+...+4^6=\dfrac{4^7-1}{3}\) 

\(\Rightarrow B-3A=4^7-3\cdot\dfrac{4^7-1}{3}=1\)

______

\(A=2^0+2^1+...+2^{2008}=2^{2009}-1\)

\(\Rightarrow B-A=2^{2009}-2^{2009}+1=1\)

_____

\(A=1+3+3^2+....+3^{2006}=\dfrac{3^{2007}-1}{2}\)

\(\Rightarrow B-2A=3^{2007}-2\cdot\dfrac{3^{2007}-1}{2}=1\)

làm ơn trả lời hộ mk với ah mai mk phải nộp bài r

theo bài ra ta có:

\(\frac{3a^2-b^2}{a^2+b^2}=\frac{3}{4}\)

=> 4( 3a² - b²) = 3( a²+ b²)

=> 12a²- 4b² = 3a² + 3b²

=> 12a²- 3a² = 3b² + 4b²

=> 9a²= 7b²

=> \(\frac{7}{9}=\frac{a^2}{b^2}\Rightarrow\sqrt{\frac{7}{9}}=\frac{a}{b}\)

vậy \(\sqrt{\frac{7}{9}}=\frac{a}{b}\)

\(\frac{3a^2-b^2}{a^2+b^2}\)=\(\frac{3}{4}\)

=>4.(3a²-b=²)=3.(a²+b²)

4.3a²-4.b²=3.a²+3.b²

12a²-4b²=3a²+3b²

12a²-3a²=4b²+3b²

9a²=7b²

\(\frac{a^2}{b^2}\)=\(\frac{7}{9}\)

=>\(\frac{a}{b}\)=\(\sqrt{\frac{7}{9}}\)

đặt a/b=t

chia cả tử mấu cho b^2

\(\Leftrightarrow\frac{3t^2-1}{t^2+1}=\frac{3}{4}\)\(12t^2-4=3t^2+3\Rightarrow9t^2=7\Rightarrow\orbr{\begin{cases}\frac{a}{b}=t=\frac{\sqrt{7}}{3}\\\frac{a}{b}=t=\frac{-\sqrt{7}}{3}\end{cases}}\)

a/b=