Question

b. (x+7) (x+9) = (x+3) (x+21)​

Answer 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

⟶(x+7)(x+9)=(x+3)(x+21)

How to solve :

Step1: First step is to open the brackets and Multiply with each and every term

Step2: Now ,make like terms together and shifts all constant term to one side.

Step3:Let the Variable alone and shifts constant to constant side .

⟶x(x+9)+7(x+9)=x(x+21)+3(x+21)

⟶x²+9x+7x+63=x²+21x+3x+63

63 lies on both sides so,it gets automatically cancelled.

⟶x²+9x+7x=x²+21x+3x

x square lies on both sides so,it gets cancelled.

⟶9x+7x=21x+3x

⟶15x=24x

⟶24x-15x=0

⟶9x=0

x=0

Check:

⟶(0+7)(0+9)

⟶0(0+9)+7(0+9)

⟶0+0+0+63

=63

Taking RHS

⟶(x+3)(x+21)

⟶(0+3)(0+21)

⟶0(0+21)+3(0+21)

⟶0+0+0+63

=63

LHS =RHS (Verified)

Answer 2

Given : Equation = (x+7) (x+9) = (x+3) (x+21)

Need To Find : The Value of x .

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$\qquad \qquad \dag\:\:\bf{Equation \::\bigg( (x + 7) (x +9) = (x + 3) (x + 21)\bigg) }$

$\Large{\gray{\bf{Let's \:Solve \:the\:Given \:Equation \::}}}$

$\qquad \longmapsto \:\:\sf{ (x + 7) (x +9) = (x + 3) (x + 21) }$

$\qquad \longmapsto \:\:\sf{ x (x +9) + 7(x + 9) = (x + 3) (x + 21) }$

$\qquad \longmapsto \:\:\sf{ x^2 +9x + 7x + 63 = (x + 3) (x + 21) }$

$\qquad \longmapsto \:\:\sf{ x^2 +9x + 7x + 63 = x (x + 21) + 3(x + 21) }$

$\qquad \longmapsto \:\:\sf{ x^2 +9x + 7x + 63 = x ^2 + 21x+ 3x + 63 }$

By Eliminating 63 from Both side :

$\qquad \longmapsto \:\:\sf{ x^2 +9x + 7x + \cancel {63} = x ^2 + 21x+ 3x + \cancel{63} }$

$\qquad \longmapsto \:\:\sf{ x^2 +9x + 7x = x ^2 + 21x+ 3x }$

By Eliminating x² from both sides :

$\qquad \longmapsto \:\:\sf{ \cancel {x^2} +9x + 7x = \cancel{x ^2} + 21x+ 3x }$

$\qquad \longmapsto \:\:\sf{ 9x + 7x = 21x+ 3x }$

$\qquad \longmapsto \:\:\sf{15x = 24x }$

$\qquad \longmapsto \:\:\sf{ 24x - 15x = 0 }$

$\qquad \longmapsto \:\:\sf{ 9x = 0 }$

$\qquad \longmapsto \:\:\sf{ x =\cancel {\dfrac{ 0}{9}} }$

$\qquad \longmapsto \:\:\cal{\purple{\underline{ x = 0 }}}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  The\:Value \:of\:x \:is\:\bf{0\: }}}}$

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V E R I F I C A T I O N :

$\qquad \qquad \dag\:\:\bf{Equation \::\bigg( (x + 7) (x +9) = (x + 3) (x + 21)\bigg) }$

Here ,

• $\qquad \longmapsto \:\:\sf{ x = 0 }$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: x=0 \:in\: Given \: Equation \::}}$

$\qquad \longmapsto \:\:\sf{ (x + 7) (x +9) = (x + 3) (x + 21) }$

$\qquad \longmapsto \:\:\sf{ (0 + 7) (0 +9) = (0 + 3) (0 + 21) }$

$\qquad \longmapsto \:\:\sf{ 0(0 + 9) +7(0 +9) = (0 + 3) (0 + 21) }$

$\qquad \longmapsto \:\:\sf{ 0 + 0 + 0 + 63 = (0 + 3) (0 + 21) }$

$\qquad \longmapsto \:\:\sf{ 63 = (0 + 3) (0 + 21) }$

$\qquad \longmapsto \:\:\sf{ 63 = 0 (0 + 21)+ 3(0+21) }$

$\qquad \longmapsto \:\:\sf{ 63 = 0 + 0 + 0 + 63 }$

$\qquad \longmapsto \:\:\cal{\purple{\underline{ 63 = 63 }}}$

Therefore,

• L.H.S = R.H.S

⠀⠀⠀⠀⠀$\therefore {\underline {\bf{ Hence, \:Verified \:}}}$

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