Question

Prove that 0.85×0.85×0.85+0.15×0.15×0.15 divided by 0.85×0.85-0.85×0.15+0.15×0.15
Question number 37 of RS Aggarwal class 9 factorisation of polynomials.

Answer 1

$\frac{0.85 \times 0.85 \times 0.85 + 0.15 \times 0.15 \times 0.15}{0.85 \times 0.85 - 0.85 \times 0.15 + 0.15 \times 0.15} =1$

Let us take 0.85 = a and and 0.15 = b

So we know that LHS

$= \frac{a \times a \times a + b \times b \times b}{a \times a - a \times b + b \times b}$

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

According to the equation,

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

So we get,

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

Since

$a^2 - ab + b^2$

is similar in numerator and denominator

We get,

$=(a + b)$

Now by replacing the values of a and b

$=0.85 + 0.15$

$=1$

$= RHS$

Hence proved.