Prove that (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

bararskzs

bararskzs

Answered question

2023-01-05

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 & Explanation

Payncchoiny5p5

Payncchoiny5p5

Beginner2023-01-06Added 12 answers

Solution:
LHS: 0.85 × 0.85 × 0.85 + 0.15 × 0.15 × 0.15 0.85 × 0.85 0.85 × 0.15 + 0.15 × 0.15
We have
a 3 + b 3 = ( a + b ) ( a 2 + b 2 a b )
Here a=0.85,b=0.15
( 0.85 + 0.15 ) ( 0.85 2 0.85 × 0.15 + 0.15 2 )
= ( 0.85 + 0.15 ) ( 0.85 2 0.85 × 0.15 + 0.15 2 ) ( 0.85 2 0.85 × 0.15 + 0.15 2 )
=0.85+0.15=1
Hence, LHS = RHS

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