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Zeroes of a Polynomial

If a - b = ...

Question

If $a - b = 4$ and $a + b = 6$ , then find $a^{2} + b^{2}$

A

25

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B

32

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C

26

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D

30

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Solution

The correct option is B $26$
Given, $a + b = 6$
Squaring both sides, we get
$(a + b)^{2} = 6^{2}$
$=> a^{2} + b^{2} + 2 a b = 36$ ------------(i)
Also $a - b = 4$
Squaring both sides, we get
$(a - b)^{2} = 4^{2}$
$=> a^{2} + b^{2} - 2 a b = 16$ ------------(ii)
Adding (i) and (ii), we get
$=> 2 (a^{2} + b^{2}) = 52$
$=> a^{2} + b^{2} = 26$

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