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: 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 know a^3+b^3=(a+b)(a^2+b^2 ab) Here a=0.85,b=0.15 (0.85+0.15)(0.85^2 ...

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Standard IX

Mathematics

Algebraic Identities

Prove that 0....

Question

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

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Solution

ANSWER:
LHS: $\frac{0.85 \times 0.85 \times 0.85 + 0.15 \times 0.15 \times 0.15}{0.85 \times 0.85 - 0.85 \times 0.15 + 0.15 \times 0.15}$

We know
$a^{3} + b^{3} = (a + b) (a^{2} + b^{2} - a b)$
Here a=0.85,b=0.15
$(0.85 + 0.15) ({0.85}^{2} - 0.85 \times 0.15 + {0.15}^{2}) = (0.85 + 0.15) \frac{({0.85}^{2} - 0.85 \times 0.15 + {0.15}^{2})}{({0.85}^{2} - 0.85 \times 0.15 + {0.15}^{2})} = 0.85 + 0.15 = 1$
Thus, LHS = RHS

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Prove that 0.85×0.85×0.85+0.15×0.15×0.150.85×0.85−0.85×0.15+0.15×0.15=1.

ANSWER: LHS:0.85×0.85×0.85+0.15×0.15×0.150.85×0.85−0.85×0.15+0.15×0.15 We know a3+b3=(a+b)(a2+b2−ab) Here a=0.85,b=0.15 (0.85+0.15)(0.852−0.85×0.15+0.152)=(0.85+0.15)(0.852−0.85×0.15+0.152)(0.852−0.85×0.15+0.152)=0.85+0.15=1 Thus, LHS = RHS

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