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Question
Find the value of x, if 14x = (47)2 − (33)2.
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Solution
Let us consider the following equation: \[14x = \left( 47 \right)^2 - \left( 33 \right)^2\]
Using the identity \[\left( a + b \right)\left( a - b \right) = a^2 - b^2\],we get:
\[14x = \left( 47 \right)^2 - \left( 33 \right)^2 \]
\[14x = \left( 47 + 33 \right)\left( 47 - 33 \right)\]
\[14x = 80 \times 14 = 1120\]
\[\Rightarrow 14x = 1120\]
\[\Rightarrow x = 80\]
(Dividing both sides by 14)
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