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If a + b = sqrt5 and a -b = sqrt3, then ...

If `a + b = sqrt5 and a -b = sqrt3`, then the value of `a^(2) + b^(2)` is

A

8

B

4

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
B
We know that `a^(2) + b^(2) = (1)/(2) xx 2 (a^(2) + b^(2))`
`= (1)/(2) {(a + b)^(2) + (a-b)^(2)}` (by formula)
`= (1)/(2) {(sqrt5)^(2) + (sqrt3)^(2)} = (1)/(2) (5 +3)`
`= (1)/(2) xx 8 4`
`:.` (b) is correct
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CALCUTTA BOOK HOUSE-QUADRATIC SURDS-Exercise -3.2
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