Question

Find the value of x, if 4x = (52)² − (48)².

Answer 1

Let us consider the following equation: \[4x = \left( 52 \right)^2 - \left( 48 \right)^2\]

Using the identity \[\left( a + b \right)\left( a - b \right) = a^2 - b^2\],we get:

\[4x = \left( 52 \right)^2 - \left( 48 \right)^2 \]

\[4x = \left( 52 + 48 \right)\left( 52 - 48 \right)\]

\[4x = 100 \times 4 = 400\]

\[\Rightarrow 4x = 400\]

\[\Rightarrow x = 100\]   (Dividing both sides by 4)