Question

If $\frac{\sqrt{7}-2}{\sqrt{7}+2}=a\sqrt{7}+b,$ find $a$ and $b$.

• A. $a=\frac{-11}{3},$ $b=\frac{4}{3}$
• B. $a=\frac{-4}{3},$ $b=\frac{11}{3}$
• C. $a=\frac{11}{3},$ $b=\frac{4}{3}$
• D. $a=\frac{4}{3},$ $b=\frac{11}{3}$

Answer 1

The correct option is B $a=\frac{-4}{3},$ $b=\frac{11}{3}$

$\left(\frac{\sqrt{7}-2}{\sqrt{7}+2}\right)\times \left(\frac{\sqrt{7}-2}{\sqrt{7}-2}\right)=\left(\frac{7+2^2-2\times 2\sqrt{7}}{7-4}\right)=\left(\frac{-4}{3}\right)\sqrt{7}+\left(\frac{11}{3}\right)\therefore a=\left(\frac{-4}{3}\right)andb=\left(\frac{11}{3}\right)$