The sum of two numbers is $9$ and their product is $20$ . Find sum of their squares.

33

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41

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67

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11

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Solution

The correct option is B $41$
Let two number be $x$ and $y$
Given,
$x + y = 9$ and
$x y = 20$
Now,
$x + y = 9$
Squaring both the sides,
$(x + y)^{2} = 9^{2}$
$=> x^{2} + y^{2} + 2 x y = 81$
$=> x^{2} + y^{2} + 2 (20) = 81$
$=> x^{2} + y^{2} + 40 = 81$
$=> x^{2} + y^{2} = 81 - 40$
$=> x^{2} + y^{2} = 41$

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