Question

If $4x-5y=16$ and $xy=12$ then the value of $64x^3-125y^3=$ is _______

A. $4648$
B. $15616$
C. $4672$
D. $4696$
E. None of these

• A. $15616$
  ⇒64$
• B. $4672$
• C. $4696$
• D. $4648$
• E. None of these

Answer 1

Answer: (A)

$\left(15616\right)$

Given $4x-5y=16$

Cubing on both sides

$\Rightarrow (4x-5y{)}^3=(16{)}^3$

$\Rightarrow 64x^3-125y^3-3\times 4x\times 5y(4x-5y)=4096$

$\Rightarrow 64x^3-125y^3-60xy(4x-5y)=4096$

$\Rightarrow 64x^3-125y^3-60\left(12\right)\left(16\right)=4096$ (Since, Given $xy=12$)

$\Rightarrow 64x^3-125y^3-11520=4096$

$\Rightarrow 64x^3-125y^3=4096+11520$

$\therefore 64x^3-125y^3=15616$