Question

$\green{ \underline{ \boxed{ \odot \mid{ \bf{question :- }}}}}$

$\leadsto$ ( 2x + 3 ) ² + ( 2x - 3 ) ² = ( 8x + 6 ) ( x + 1 ) + 22


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Answer 1

Answer:

Solution:

(2x+3)² + (2x-3)² = (18x+6)(x-1)+22

using (a + b)² = a + 2ab + b²

=> 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

Answer 2

$\LARGE\fbox\red{A}\fbox\pink{n}\fbox\purple{S}\fbox\green{w}\fbox\blue{E}\fbox\orange{r}$

$\:$

$\tt{(2x+3)²+(2x-3)²=(8x+16)(x+1)+22}$

$\:$

$\tt\red{UsiNg=(a+b)²=a+2ab+b²}$

$\leadsto$ $\tt\green{4x²+12x+9+4x²-12x+9=8x²-8x+6x-6+22}$

$\leadsto$ $\tt\green{8x²+18=8x²-2x+16}$

$\implies$ $\tt\red{Cancelling\:8x²\: frm\:both\:sides:-}$

$\leadsto$ $\tt\green{18=-2x+16}$

$\leadsto$ $\tt\green{2=-2x}$

$\implies$ $\tt\red{x=-1}$