Question

The value of \$\frac{6.35 \times 6.35 \times 6.35 + 3.65 \times 3.65 \times 3.65}{63.5 \times 63.5 + 36.5 \times 36.5 - 63.5 \times 36.5}$ is equal to

• A. 0.01
• B. 10
• C. 0.1
• D. 1

Answer 1

Answer:

C. 0.1

Solution:

Concept used:

(a³ + b³) = (a + b) $\times$ (a² + b² – ab)

Calculation:

$⇒ \frac{6.35 \times 6.35 \times 6.35 + 3.65 \times 3.65 \times 3.65}{63.5 \times 63.5 + 36.5 \times 36.5 - 63.5 \times 36.5}$

$⇒ \frac{{(6.35 )^3 + (3.65)^3}}{{(6.35 \times 10)^2 + (3.65 \times 10)^2 - 6.35 \times 10 × 3.65 \times 10}}$

⇒ $\frac{{(6.35 )^3 + (3.65)^3}}{{(6.35 \times 10)^2 + (3.65 \times 10)^2 - 6.35 \times 10 × 3.65 \times 10}}$

⇒ $\frac{{ {(6.35 \: + \:3.65) \times [(6.35)^2 + (3.65)^2 - 6.35 × 3.65}]}}{100{[(6.35)^2 + (3.65)^2 - 6.35 × 3.65}]}$

⇒ $\frac{(6.35+3.65)}{100}$

⇒ $\frac{10}{100}$

⇒ 0.1