Question

The value of $\frac{0.9\times 0.9\times 0.9+0.1\times 0.1\times 0.1}{0.9\times 0.9-0.9\times 0.1+0.1\times 0.1}$ on simplification is

• A. 0
• B. -1
• C. 2
• D. 1

Answer 1

The correct option is D 1

$\frac{0.9\times 0.9\times 0.9+0.1\times 0.1\times 0.1}{0.9\times 0.9-0.9\times 0.1+0.1\times 0.1}$

=$\frac{(0.9{)}^3+(0.1{)}^3}{(0.9{)}^2-0.9\times 0.1+(0.1{)}^2}$

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

Then $\frac{(0.9+0.1)\left[\right(0.9{)}^2-0.9\times 0.1+\left(0.1{)}^2\right]}{(0.9{)}^2-0.9\times 0.1+(0.1{)}^2}=(0.9+0.1)=1$