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Simplify the Following Using the Identities: 8 . 63 × 8 . 63 − 1 . 37 × 1 . 37 0 . 726 - Mathematics

Answer in Brief

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

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Solution

 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.

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APPEARS IN

RD Sharma Class 8 Maths
Chapter 6 Algebraic Expressions and Identities
Exercise 6.6 | Q 5.5 | Page 43
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