Question

$\frac{0.83\times 0.83\times 0.83+0.17\times 0.17\times 0.17}{0.83\times 0.83-0.83\times 0.17+0.17\times 0.17}$ is equal to

• A. $1$
• B. $(0-83{)}^3+(0.17{)}^3$
• C. $0$
• D. none of these

Answer 1

Answer: (A)

$\frac{0.83\times 0.83\times 0.83+0.17\times 0.17\times 0.17}{0.83\times 0.83-0.83\times 0.17+0.17\times 0.17}$

$=\frac{(0.83{)}^3+(0.17{)}^3}{(0.83{)}^2-(0.83\left)\right(0.17)+(0.17{)}^2}$ which is in the form of $\frac{a^3+b^3}{a^2-ab+b^2}$

$=\frac{(0.83+0.17)\left[\right(0.83{)}^2-\left(0.83\right)\left(0.17\right)+\left(0.17{)}^2\right]}{\left[\right(0.83{)}^2-\left(0.83\right)\left(0.17\right)+\left(0.17{)}^2\right]}$ ..... $[\because \frac{a^3+b^3}{a^2-ab+b^2}=\frac{(a+b)(a^2-ab+b^2)}{(a^2-ab+b^2)}]$

$=0.83+0.17=1$
Hence, option A is correct.