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13. If a+b=9 and ab=-22,find i) a2-b2
Asked by swarup.ghosh21 | 01 May, 2023, 10:27: AM
We know that a2 - b2 = (a + b) (a - b)
Given: a + b = 9
ab = -22

Let us find (a - b)
We know the identity,
(a - b)2 = a2 + b2 - 2ab
(a - b)2 = (a + b)2 - 2ab - 2ab
(a - b)2 = (a + b)2 - 4ab
(a - b)2 = (9)2 - 4(-22)
(a - b)2 = 81 + 88
(a - b)2 = 169
(a - b)2 = (13)2
So,
a - b = 13
Therefore the value of a2 - b2
= (a + b) (a - b)
= 9 x 13
= 117

Answered by | 01 May, 2023, 05:50: PM

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