Question

The value of \(\frac{{85.2 \times 85.2\; \times 85.2 - 75.2 \times 75.2 \times 75.2}}{{8.52 \times 8.52 + 7.52 \times 7.52 + 8.52 \times 7.52\;}}\) is equal to:
1. 100
2. 1000
3. 10
4. 10000

Answer 1

Correct Answer - Option 2 : 1000

Given:

\(\frac{{85.2 × 85.2\; × 85.2 - 75.2 × 75.2 × 75.2}}{{8.52 × 8.52 + 7.52 × 7.52 + 8.52 × 7.52\;}}\)

Formula used:

a³ - b³ = (a - b)(a² + b² + ab)

Calculation:

\(\frac{{85.2 × 85.2\; × 85.2 - 75.2 × 75.2 × 75.2}}{{8.52 × 8.52 + 7.52 × 7.52 + 8.52 × 7.52\;}}\)

⇒ \(\frac{{85.2^3 - 75.2^3}}{{8.52^2 + 7.52^2 + 8.52 × 7.52\;}}\)

⇒ \(\frac{{(85.2 - 75.2)(85.2^2 + 75.2^2 + 85.2 × 75.2)}}{\frac{1}{100}({85.2^2 + 75.2^2 + 85.2 × 75.2)}}\)

⇒ 100 × (85.2 - 75.2)

⇒ 100 × 10 = 1000

∴ The correct answer is 1000.

 

(8.52 × 8.52 + 7.52 × 7.52 + 8.52 × 7.52) = (1/100)(85.2 × 85.2 + 75.2 × 75.2 + 85.2 × 75.2)