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प्रश्न
Simplify the following using the formula: (a − b)(a + b) = a2 − b2: 9.8 × 10.2
उत्तर
Here, we will use the identity \[(a - b)(a + b) = a^2 - b^2\]
Let us consider the following product: \[9 . 8 \times 10 . 2\]
\[\because \frac{9 . 8 + 10 . 2}{2} = \frac{20}{2} = 10\]; therefore, we will write the above product as:
\[9 . 8 \times 10 . 2\]
\[ = \left( 10 - 0 . 2 \right)\left( 10 + 0 . 2 \right)\]
\[ = \left( 10 \right)^2 - \left( 0 . 2 \right)^2 \]
\[ = 100 - 0 . 04\]
\[ = 99 . 96\]
Thus, the answer is 99.96.
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