Question

If 4x+5y=23 and xy =6,find the value of 16x^2+25y^2.

Answer 1

4x + 5y = 23

xy = 6, => y = 6 / x

Substituting value of y = 6 / x in the first equation we get,

4x + 5 ( 6 / x ) = 23

4x + 30 / x = 23

Taking LCM we get,

4x² + 30 / x = 23

4x² + 30 = 23 x

=> 4x² - 23x + 30 = 0

=> 4x - 15x - 8x + 30 = 0

=> x ( 4x - 15 ) - 2 ( 4x - 15 ) = 0

=> ( 4x - 15 ) ( x - 2 ) = 0

=> x = 15 / 4 ; 2

Taking X = 2 we get y = 6 / 2 = 3

So value of 16x² + 25y² is :

16 ( 2 )² + 25 ( 3 )²

16 * 4 + 25 * 9

64 + 225

289