If `a + b = sqrt5 and a -b = sqrt3`, then the value of `a^(2) + b^(2)` isA. 8B. 4C. 2D. 1

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

1.	If `a + b = sqrt5 and a -b = sqrt3`, then the value of `a^(2) + b^(2)` isA. 8B. 4C. 2D. 1
Answer» Correct Answer - 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

If `x = 2 + sqrt3, y = 2 - sqrt3`, then find the simpliest value of (a) `x - (1)/(x)`, (b) `y^(2) + (1)/(y^(2))`, (c) `x^(3) - (1)/(x^(3))`, (d) `xy + (1)/(xy)`
If `m + (1)/(m) = sqrt3`, then find the simpliest value of (i) `m^(2) + (1)/(m^(2))` and (ii) `m^(3) + (1)/(m^(3))`:
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`sqrt7 - sqrt5` is a binomial surd
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Express in the form of like surds: `root(3)(4), root(6)(5), 2sqrt3`.