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Solving a Quadratic Equation by Factorization Method

If x+y=8,xy...

Question

If $x + y = 8, x y = 15$ , then the value of $x^{2} + y^{2}$ will be-

32

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34

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36

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38

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Solution

The correct option is A $34$
Since $(x + y)^{2} = x^{2} + y^{2} + 2 x y$ ,
where $x + y = 8$
and $x y = 15$ (Given) then after
Substitution the values, we get
$64 = x^{2} + y^{2} + 30$
$\Rightarrow x^{2} + y^{2} = 34$

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