If $x + y = 9$ and $x y = 16$ , find the value of $(x^{2} + y^{2})$ .

49

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7

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9

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4

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Solution

The correct option is A $49$
Given, $x + y = 9$ and $x y = 16$ .

We know, $(a + b)^{2} = a^{2} + 2 a b + b^{2}$ .

Then,
$(x + y) ² = x ² + 2 x y + y ²$
$⟹$ $(9) ² = x ² + 2 (16) + y ²$
$⟹$ $81 = x ² + 32 + y ²$
$⟹$ $x ² + y ² = 81 - 32 = 49$ .

Therefore, option $A$ is correct.

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