Question

If 64x²+y²=72 and xy=2 find {4x+y_2}²

Answer 1

64 x^2 + y^2 = 72 , xy = 2

( 4x + y /2 )^2 = ?

use identity :

( a + b )^2 = a^2 + 2 ab + b^2

here a = 4x , b = y /2

( 4x + y/ 2 )^2

=(4x)^2 + 2 (4x) ( y /2 ) + ( y/ 2)^2

=16 x^2 + 4 xy + y^2/4

=(64 x^2 + 16 xy + y^2 ) / 4

={ ( 64 x^2 + y^2 ) + 16xy } / 4

={ 72 + 16 (2) } / 4 = ( 72 + 32 ) / 4

=104 / 4 = 26

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Your Answer : 26
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