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Quadratic Formula

If a2+b2=13...

Question

If $a^{2} + b^{2} = 13$ and $a b = 6$ find $3 {(a + b)}^{2} - 2 {(a - b)}^{2}$ .

A

14

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B

89

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C

45

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D

73

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Solution

The correct option is D $73$
$3 {(a + b)}^{2} - 2 {(a - b)}^{2}$
We know,
$(a + b)^{2} = a^{2} + b^{2} + 2 a b$
$= 13 + 2 (6)$
$= 13 + 12$
$= 25$
$=> (a + b) = \pm \sqrt{25}$
$=> (a + b) = \pm 5$
Again,
$(a - b)^{2} = a^{2} + b^{2} - 2 a b$
$= 13 - 2 (6)$
$= 13 - 12$
$= 1$
$=> (a - b) = \pm 1$
Putting the values, we get,
$3 {(\pm 5)}^{2} - 2 {(\pm 1)}^{2}$
$= 75 - 2$
$= 73$

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