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