Haryana Police Constable Model Paper 2

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Question : 10 of 100

Marks: +1, -0

If

(\a^{2} + \b^{2}) = 97

and

\ab = 36

, find the value of

(\a^{2} - \b^{2})

.

0
65
135
320

Solution:

∵

(\a + \b)^{2}= (\a^{2} + \b^{2}) + 2\ab

⇒

(\a + \b)^{2} = 97 + 2(36) = 169

⇒

(\a + \b) = √169 = 13

Also,
∵

(\a^{2} - \b^{2}) = (\a^{2} + \b^{2})-2\ab

⇒

(\a^{2} - \b^{2}) =

97-2 (36) = 25

⇒

(\a-\b) = √25 = 5

∴

(\a^{2} - \b^{2}) = (\a + \b)(\a-\b) = 13 × 5 = 65

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