Question

If $64a^2+36b^2=400,ab=4$ , then $8a+6b$ is:

• A. 26
• B. 28
• C. 22
• D. None of the above

Answer 1

Answer: (B)

28

Given $64a^2+36b^2=400,ab=4$

We know

$(a+b{)}^2=a^2+b^2+2ab$

therefore,

$(8a+6b{)}^2=(8a{)}^2+(6b{)}^2+2(8a\left)\right(6a)$

$=64a^2+36b^2+96ab$

$=400+96\times 4$

$=400+384$

$(8a+6b{)}^2=784$

$8a+6b=\sqrt{784}$

$8a+6b=28$