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Using a^2-b^2=(a+b) (a-b), find (i) 5...

Using `a^2-b^2=(a+b) (a-b),` find (i) `51^2-49^2` (ii) `(1.02)^2 - (0.98)^2` (iii) `153^2 - 147^2` (iv) `12.1^2 - 7.9^2`

Text Solution

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Using the algebraic identity `a^2 - b^2 = (a + b)(a - b)`
`(i) 51^2 – 49^2`
`= (51 + 49)(51 - 49)`
`= (100)(2)`
`= 200`
`(ii) (1.02)^2 - (0.98)^2`
`= (1.02 + 0.98)(1.02 - 0.98)`
`= (2)(0.04)`
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