Question

Evaluate: $\frac{2.3\times 2.3\times 2.3-1}{2.3\times 2.3+2.3+1}$

• A. 0.9
• B. 1.3
• C. 2.2
• D. 3.3

Answer 1

The correct option is A 0.9

$\frac{2.3\times 2.3\times 2.3-1}{2.3\times 2.3\times 2.3+1}$

Using $a^3-b^3=(a-b)(a^2+ab+b^2)$

and $a^3+b^3=(a+b)(a^2-ab+b^2)$ we get

$=\frac{(2.3-1)\left(\right(2.3{)}^2+\left(2.3\right)\left(1\right)+(1{)}^2}{(2.3+1)\left(\right(2.3{)}^2-\left(2.3\right)\left(1\right)+(1{)}^2}$

$=\frac{\left(1.3\right)(5.29+2.3+1)}{\left(3.3\right)(5.29-2.3+1}$

$=\frac{\left(1.3\right)\left(8.59\right)}{\left(3.3\right)\left(3.99\right)}$

$=\frac{11.167}{13.167}$

$=0.9$