Question

What will come in place of '?'

 \(\frac{(469\ +\ 174)^2\ -\ (469\ -\ 174)^2}{469\ \times\ 174}=?\)

1. 295
2. 4
3. 2
4. 643

Answer 1

Correct Answer - Option 2 : 4

Given:

\(\frac{(469\ +\ 174)^2\ -\ (469\ -\ 174)^2}{469\ \times\ 174}=?\)

Concept Used:

a² - b² = (a + b)(a - b)

Calculation:

\(\frac{(469\ +\ 174)^2\ -\ (469\ -\ 174)^2}{469\ \times\ 174}=?\)

⇒ \(\frac{(469 +174 + 469 -174)[(469 + 174) - (469 - 174)]}{469 × 174}\)

⇒ \(\frac{(2 × 469)(469 +174 -469 +174)}{469 × 174}\)

⇒ \(\frac{(2 × 469 × 2 × 174)}{469 × 174}\)

⇒ 2 × 2

⇒ 4

∴ The value that will come in place of '?' is 4.