Question

\(\dfrac{(5.5)^4 - (3.5)^4}{(5.5)^2 + (3.5)^2}\) is equal to:
1. 180
2. 18
3. 42.5
4. 1.8

Answer 1

Correct Answer - Option 2 : 18

Given 

\(\dfrac{(5.5)^4 - (3.5)^4}{(5.5)^2 + (3.5)^2}\)

Formula Used 

a² - b² = (a + b) (a - b)

Calculation 

\(\dfrac{(5.5)^4 - (3.5)^4}{(5.5)^2 + (3.5)^2}\)

⇒ \({[(5.5)^2 + (3.5)^2] \;\times \;[(5.5)^2 - (3.5)^2]} \over (5.5)^2 + (5.5)^2\)

⇒ (5.5)2 - (3.5)²

⇒ (5.5 + 3.5)(5.5 - 3.5)

⇒ 9 × 2 = 18 

∴ The value is 18