Math, asked by rianndsouza4, 1 year ago

Solve by factorisation method
(2x+3)square =16

Answers

Answered by Mihir1001
2

\huge{\underline{\mathfrak{\textcolor{blue}{Answer :}}}}

\huge\boxed{\fcolorbox{red}{#ffdfff}{x = -7/2  or  x = 1/2}}

\huge{\underline{\mathcal{\textcolor{red}{Step-by-step-explanation :}}}}

\huge{\underline{\mathtt{\textcolor{violet}{Given :-}}}}

  •  {(2x + 3)}^{2}  = 16

\huge{\underline{\mathtt{\textcolor{green}{To \:  \: Find :-}}}}

  • Factors of the equation
  • Roots of the equation

\huge{\underline{\mathtt{\textcolor{teal}{Concept \:  \: used:-}}}}

  • Factorisation of Polynomials

\huge{\underline{\mathtt{\textcolor{blue}{Solution :-}}}}

We have,

 \longmapsto  {(2x + 3)}^{2}  = 16

 \implies  {(2x)}^{2}  + 2(2x)(3) +  {(3)}^{2}  = 16

 \implies  4 {x}^{2}  + 12x +  9 = 16

 \implies  4 {x}^{2}  + 12x +  9 - 16 = 0

 \implies  4 {x}^{2}  + 12x - 7 = 0

 \implies  4 {x}^{2}  + (14 - 2)x - 7 = 0

 \implies  4 {x}^{2}  + 14x - 2x - 7 = 0

 \implies  2x(2x + 7) - 1(2x + 7) = 0

 \implies  (2x + 7)(2x - 1) = 0

 \implies  (2x + 7) = 0 | or \:  (2x - 1) = 0

 \implies  2x =  - 7 \:  \:  \:  \:  \:  \:  \: |  \implies  2x = 1

 \implies  x = \large{ -  \frac{7}{2}  \:  \:  \:  \: } |  \implies  x = \large{ \frac{1}{2} }

\huge{\underline{\mathtt{\textcolor{magenta}{Conclusion :-}}}}

  • \large{x =  -  \frac{7}{2} }

  • OR

  • \large{x =  \frac{1}{2} }

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