Question

If $5a\sqrt{b}-\frac{3}{2b\sqrt{a}}=12$ and $a=8b$, then the value of $25a^{2}b+\frac{9}{4a{b}^2}$ is ?

• A. $144-15\sqrt{8}$
• B. $144+15\sqrt{8}$
• C. $15\sqrt{8}-144$
• D. $-15\sqrt{8}-144$

Answer 1

Answer: (B)

$144+15\sqrt{8}$

Given,

$5a\sqrt{b}-\frac{3}{2b\sqrt{a}}=12$

Formula,

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

squaring the given on both sides,

$25a^{2}b+\frac{9}{4b^{2}a}-2\left(5a\sqrt{b}\right)\left(\frac{3}{2b\sqrt{a}}\right)=144$

$25a^{2}b+\frac{9}{4b^{2}a}=144+2\left(5a\sqrt{b}\right)\left(\frac{3}{2b\sqrt{a}}\right)$

$=144+15\sqrt{\frac{a}{b}}$

$=144+15\sqrt{\frac{8b}{b}}$

$=144+15\sqrt{8}$