Question

Find the value of x, if 14x = (47)² − (33)².

Answer 1

 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)