Question

(2x+3)²+(2x-3)²=(8x+6)(x-1)+22

Answer 1

GIVEN :

The equation is $(2x+3)^2+(2x-3)^2=(8x+6)(x-1)+22$

TO FIND :

The value of x in the given equation

SOLUTION :

Given equation is $(2x+3)^2+(2x-3)^2=(8x+6)(x-1)+22$

Solving  the equation $(2x+3)^2+(2x-3)^2=(8x+6)(x-1)+22$ as below :

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

By using the Algebraic identities :

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

ii) $(a-b)^2=a^2-2ab+b^2$

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

$2^2x^2+12x+9+2^2x^2-12x+9=(8x+6)(x-1)+22$

By using the Distributive property :

(a+b)(x+y)=a(x+y)+b(x+y)

$4x^2+4x^2+18=8x(x-1)+6(x-1)+22$

By using the Distributive property :

(a)(x-y)=ax-ay

$8x^2+18=8x(x)+8x(-1)+6(x)+6(-1)+22$

$8x^2+18=8x^2-8x+6x-6+22$

18=-2x+16

-2x+16-18=0

-2x-2=0

-2x=2

$x=-\frac{2}{2}$

∴ x=-1

∴ the value of x in the given equation is -1

Answer 2

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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