Math, asked by Anonymous, 5 months ago

\huge\tt\red{\bold{\underline{\underline{❥Question᎓}}}}factorise it by completing the square method:
9 {x}^{2} - 15x + 6 = 0

Answers

Answered by Anonymous
18

\huge\tt\red{\bold{\underline{\underline{❥Question᎓}}}}factorise it by completing the square method:

9 {x}^{2} - 15x + 6 = 0

\huge\mathcal{Answer}

⟹\bold{9 {x}^{2}  - 15x + 6 = 0}

⟹\bold{9 {x}^{2}  - 15x =  - 6}

⟹ \bold{{x}^{2}  -  \frac{15}{9} x =  -  \frac{6}{9}}

⟹\bold{ {x}^{2}  -  \frac{5}{3} x =   - \frac{2}{3}}

⟹\bold{ {x}^{2}  -  \frac{5}{3} x +  { (\frac{5}{6} )}^{2}  = -   \frac{2}{3}  +  { (\frac{5}{6} )}^{2}}

⟹\bold{ {(x -  \frac{5}{6}) }^{2}  =  -  \frac{2}{3}  +  \frac{25}{36} }

 ⟹\bold{{(x -  \frac{5}{6}) }^{2}  =  \frac{ - 24 + 25}{36} }

\bold{ {(x -  \frac{5}{6} )}^{2}  =  \frac{1}{36}  =  {( \frac{1}{6} )}^{2}}

Taking square root on both sides,we get

⟹\bold{(x -  \frac{5}{6} ) = ± \frac{1}{6} }

⟹\bold{x -  \frac{5}{6}  =  \frac{1}{6} }

⟹\bold{x -  \frac{5}{6}  =  -  \frac{1}{6} }

⟹\bold{x =  \frac{5}{6}  +  \frac{1}{6} }

⟹\bold{x =  \frac{5}{6}  -  \frac{1}{6}}

⟹\bold{\red{\boxed{x = 1}}}

⟹\bold{\red{\boxed{x =  \frac{4}{6}  =  \frac{2}{3}}}}

∴The solutions to given equation are\bold{\red{1}}and \bold{\red{2/3}}

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Answered by jaydip1118
1

\rm\underline\bold{Answer \purple{\huge{\checkmark}}}

∴The solutions to given equation are 1 and 2/3

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