Question

Prove that 0.85×0.85×0.85+0.15×0.15×0.15/0.85×0.85-0.85×0.15+0.15×0.15=1

Answer 1

it can be written as

(0.85³+0.15³)/ (0.85³-0.15³)

[a³+b³= (a+b)³-3ab(a+b)]

and [ a³-b³ = (a-b)³ -3ab(a-b)]

so ,

[(0.85+0.15)³ -3×0.85×0.15(0.85+0.15) ]/ (0.85-0.15)³ - 3×0.85×0.15 (0.85-0.15)

1-0.3825(1)/ 0.7³- 0.3825(0.7)

= 1.02 ≈ 1

hope it helps you