Question

If $a=\frac{2b+13}{5}$ and $b=\frac{30}{a}$, then the value of $125a^3-8b^3$ is

• A. $13789$
• B. $13897$
• C. $19766$
• D. $89713$

Answer 1

The correct option is B $13897$

$a=\frac{2b+13}{5}$

$\Rightarrow 5a=2b+13$ …………$\left(1\right)$

$\Rightarrow (5a{)}^3=(2b+13{)}^2$

$\Rightarrow 125a^3=8b^3+2197+3\times 2b\times 13(2b+13)$

$\Rightarrow 125a^3=8b^3+2197+78b\left(5a\right)$ from $\left(1\right)$

$\Rightarrow 125a^3=8b^3+2197+390ab$

We have $b=\frac{30}{a}$

$\Rightarrow ab=30$

$\therefore 125a^3=8b^3+2197+390\times 30=8b^3+13897$

$125a^3-8b^3=8b^3+13897-8b^3$

$=13897$.