Question

$\frac{(0.137{)}^3+(0.113{)}^3}{(0.137{)}^2-(0.137\left)\right(0.113)+(0.113{)}^2}=$

Answer 1

Finding value of expression:

The given expression is $\frac{(0.137{)}^3+(0.113{)}^3}{(0.137{)}^2-(0.137\left)\right(0.113)+(0.113{)}^2}$.

We know identity, $a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)$.

So, $(0.137{)}^3+(0.113{)}^3=\left(0.137+0.113\right)\left[{\left(0.137\right)}^2-\left(0.137\right)\left(0.113\right)+{\left(0.113\right)}^2\right]--\left(1\right)$

Substituting equation (1) in the given expression we have:

$$\begin{gathered} \frac{(0.137{)}^3+(0.113{)}^3}{(0.137{)}^2-(0.137\left)\right(0.113)+(0.113{)}^2}=\frac{(0.137+0.113)[{\displaystyle (}{\displaystyle 0}{\displaystyle .}{\displaystyle 137}{\displaystyle {)}^2}{\displaystyle -}{\displaystyle (}{\displaystyle 0}{\displaystyle .}{\displaystyle 137}{\displaystyle )}{\displaystyle (}{\displaystyle 0}{\displaystyle .}{\displaystyle 113}{\displaystyle )}{\displaystyle +}{\displaystyle (}{\displaystyle 0}{\displaystyle .}{\displaystyle 113}{\displaystyle {)}^2]}}{(0.137{)}^2-(0.137\left)\right(0.113)+(0.113{)}^2} \\ =\left(0.137+0.113\right) \\ =0.25 \end{gathered}$$

Hence, $\frac{(0.137{)}^3+(0.113{)}^3}{(0.137{)}^2-(0.137\left)\right(0.113)+(0.113{)}^2}=0.25$.