If $a^{2} + b^{2} = 34$ and $a b = 12$ , find $3 (a + b)^{2} + 5 (a - b)^{2}$ .

224

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132

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179

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245

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Solution

The correct option is A 224
$3 {(a + b)}^{2} + 5 {(a - b)}^{2}$
$= 3 [a^{2} + b^{2} + 2 a b] + 5 (a^{2} + b^{2} - 2 a b)$
Putting the value,we get,
$= 3 [34 + 2 (12)] + 5 [34 - 2 (12)]$
$= 3 (34 + 24) + 5 (34 - 24)$
$= 3 (58) + 5 (10)$
$= 174 + 50$
$= 224$

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