Question

When $a=\frac{4}{3}$, the value of $27a^3-108a^2+144a-317$ is

• A. $261$
• B. $-253$
• C. $-245$
• D. $0$

Answer 1

The correct option is B $-253$

$a=\frac{4}{3}\Rightarrow 3a=4\Rightarrow 3a-4=0$
On cubing both sides,
$27a^3+3(3a{)}^2-(-4)+3\times 3a(-4{)}^2-64=0$
$\Rightarrow 27a^3-108a^2+144a-64=0$
$27a^3-108a^2+144a-64-253=-253$
Hence, $27a^3-108a^2+144a-317=-253$.