Question

The value of $\frac{55^3 + 45^3}{55^2 - 55 \times 45 + 45^2}$ is:

• A. 100
• B. 105
• C. 125
• D. 75

Hint:

Whenever you see $a^3 + b^3$ over $a^2 - ab + b^2$, the result is always $a + b$.

Answer 1

The Correct Option is A

Step 1: Recognise identity We have $a^3 + b^3 = (a+b)(a^2 - ab + b^2)$. Step 2: Cancel common factor Here $a = 55$, $b = 45$, denominator = $a^2 - ab + b^2$. So value = $a+b = 100$.