Question

(2x + 3)² + (2x - 3)² = (8x + 6)(x - 1) + 22 ; x =?

Answer 1

Given :   (2x+3)²+(2x-3)²=(8x+6)(x-1)+22

To find : Solve for x

Solution:

(2x+3)²+(2x-3)²=(8x+6)(x-1)+22

using (a + b)² = a² + 2ab + b²

(a - b)² = a² -2ab + b²

and (a + b)(c -d) = ac - ad + bc - bd

=> 4x² + 12x + 9  + 4x² - 12x + 9   =  8x² -8x + 6x - 6  + 22

=> 8x²  + 18 = 8x²  -2x + 16

Cancelling 8x² from both sides

=> 18 =  -2x + 16

=> 2 = - 2x

=> x = - 1

Verification :

LHS = (2x+3)²+(2x-3)²

= (-2 + 3)² + (-2 - 3)²

= 1 + 25

= 26

RHS  = (8x+6)(x-1)+22

= (-8 + 6)(-1 - 1)  + 22

= (-2)(-2) + 22

= 4 + 22

= 26

LHS = RHS = 26

Verified

x = -1

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