Simplify: \(\frac{(76+84)^2-(76-84)^2}{76 \times 84}\) = ?

Question

Question

This question was previously asked in

UPSSSC PET Official Paper (Held on: 16 October 2022 Shift 2)

Answer 1

Given:

\(\dfrac{(76+84)^2-(76-84)^2}{76 \times 84}\)

Formula used:

(a + b)² - (a - b)² = 4ab

Calculations:

(a + b)2 - (a - b)2

⇒ a² + b² + 2ab - {a² + b² - 2ab}

⇒ 2ab + 2ab = 4ab

Now, \(\dfrac{(76+84)^2-(76-84)^2}{76 \times 84}\)

⇒ \(\dfrac{4 × 76 × 84}{76 × 84}\) = 4

∴ The answer is 4

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