Question

$if \: p { }^{2} + q { }^{2} = 252 \: \: and \: \: p + q \: = 16 \: \\ evaluate \: pq$
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Answer 1

Solution :

p² + q² = 252

&

p + q = 16 .

Squaring the second equation ;

( p + q )² = 256

=> p² + q² + 2pq = 256

But , p² + q² = 252 , as mentioned in the question .

Hence ,

252 + 2pq = 256

=> 2pq = 256 - 252

=> 2pq = 4

=> pq = 2 .

Thus , the required value of pq is 12 .

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Additional Information :

( a + b )² = a² + 2ab + b²

( a - b )² = a² - 2ab + b²

( a + b )( a - b ) = a² - b²

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