Question

Find the value of $p$ in $(51{)}^2-(49{)}^2=100p$.

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

The correct option is A 2

Given: $(51{)}^2-(49{)}^2=100p$

This is in the form of $(a{)}^2-(b{)}^2$ where a = 51 and b = 49.
We know that $(a{)}^2-(b{)}^2=(a+b)(a-b)$
$\therefore (51{)}^2-(49{)}^2=(51+49)(51-49)=100p$
$=100\times 2=100p$
$\Rightarrow p=2$