Math, asked by nayank734, 2 months ago

x²+x+1=(x+1/2)² + (√3/2)² how is any formula to convert it into that​

Answers

Answered by mathdude500
3

The method is called Completing Squares Method

\tt \longrightarrow \:  {x}^{2}  + x + 1

On adding and Subtracting square of 1/2 the coefficient of x, we get

\tt \longrightarrow \:  {x }^{2}  + x + \dfrac{1}{4}  - \dfrac{1}{4}  + 1

\tt \longrightarrow \: ( {x}^{2}  + x + \dfrac{1}{4} ) + \dfrac{4 - 1}{4}

\tt \longrightarrow \:  { \bigg(x + \dfrac{1}{2}  \bigg)}^{2}  + \dfrac{3}{4}

\tt \longrightarrow \: { \bigg(x + \dfrac{1}{2}  \bigg)}^{2}   + { \bigg(\dfrac{ \sqrt{3} }{2}  \bigg)}^{2}

\large{\boxed{\boxed{\bf{Hence, Proved}}}}

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