Question

Evaluate: $\frac{(2.3{)}^3-0.027}{(2.3{)}^2+0.69+0.09}$

• A. $1$
• B. $2$
• C. $4$
• D. None of these

Answer 1

The correct option is B $2$

$\frac{{\left(2.3\right)}^3-0.027}{{\left(2.3\right)}^2+0.69+0.09}$

We know, $a^3-b^3=(a^2+ab+b^2)(a-b)$

$\Rightarrow a^2+ab+b^2=\frac{(a^3-b^3)}{(a-b)}$

Denominator can be rewritten as,

$\Rightarrow {\left(2.3\right)}^2+\left(2.3\right)\left(0.3\right)+{\left(0.3\right)}^2=\frac{{\left(2.3\right)}^3-{\left(0.3\right)}^3}{(2.3-0.3)}$

$=\frac{{\left(2.3\right)}^3-0.027}{{\left(2.3\right)}^3+{\left(0.3\right)}^3}\times (2.3-0.3)$

$=\frac{{\left(2.3\right)}^3-{\left(0.3\right)}^3}{{\left(2.3\right)}^3-{\left(0.3\right)}^3}\times (2.3-0.3)$

$=2.$

Hence, the answer is $2.$