Question

Simplify the following using the identities: \[\frac{8 . 63 \times 8 . 63 - 1 . 37 \times 1 . 37}{0 . 726}\]

Answer 1

 Let us consider the following expression: \[\frac{8 . 63 \times 8 . 63 - 1 . 37 \times 1 . 37}{0 . 726} = \frac{8 . {63}^2 - 1 . {37}^2}{0 . 726}\]

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

\[\frac{8 . 63 \times 8 . 63 - 1 . 37 \times 1 . 37}{0 . 726} = \frac{8 . {63}^2 - 1 . {37}^2}{0 . 726} = \frac{\left( 8 . 63 + 1 . 37 \right)\left( 8 . 63 - 1 . 37 \right)}{0 . 726}\]

\[\Rightarrow \frac{8 . 63 \times 8 . 63 - 1 . 37 \times 1 . 37}{0 . 726} = \frac{\left( 8 . 63 + 1 . 37 \right)\left( 8 . 63 - 1 . 37 \right)}{0 . 726}\]

\[ \Rightarrow \frac{8 . 63 \times 8 . 63 - 1 . 37 \times 1 . 37}{0 . 726} = \frac{\left( 8 . 63 + 1 . 37 \right)\left( 8 . 63 - 1 . 37 \right)}{0 . 726}\]

\[ \Rightarrow \frac{8 . 63 \times 8 . 63 - 1 . 37 \times 1 . 37}{0 . 726} = \frac{10 \times 7 . 26}{0 . 726}\]

\[ \Rightarrow \frac{8 . 63 \times 8 . 63 - 1 . 37 \times 1 . 37}{0 . 726} = \frac{10 \times {7 . 26}^{10}}{0 . 726}\]

\[ \Rightarrow \frac{8 . 63 \times 8 . 63 - 1 . 37 \times 1 . 37}{0 . 726} = 100\]

Thus, the answer is 100.