Question

If $a=\sqrt{6}+\sqrt{5};b=\sqrt{6}-\sqrt{5}$, then find the value of $2a^2-5ab+2b^2$.

• A. $36$
• B. $37$
• C. $39$
• D. $41$

Answer 1

The correct option is C $39$

Given $a=\sqrt{6}+\sqrt{5};b=\sqrt{6}-\sqrt{5}$

Consider, $2a^2-5ab+2b^2=2(\sqrt{6}+\sqrt{5}{)}^2-5(\sqrt{6}+\sqrt{5}\left)\right(\sqrt{6}-\sqrt{5})+2(\sqrt{6}-\sqrt{5}{)}^2$

$=2(6+5+2\sqrt{5}\sqrt{6})-5(6-5)+2(6+5-2\sqrt{6}\sqrt{5})$

$=2\left(11\right)-5+2\left(11\right)=44-5=39$

$\therefore$ $2a^2-5ab+2b^2=39$
Hence, option C is correct.