Question

if (x^2+x+1) is written in the form (x+1/2)^2+q^2 find the possible value of q
pls guys help to do this sum​

Answer 1

$\underline{\bigstar\:\textsf{Given :}}$

• $\sf \bigg(x^2+x+1\bigg)= \bigg(x+\dfrac{1}{2}\bigg)^2+q^2$

$\underline{\bigstar\:\textsf{To Find :}}$

• Value of q

$\underline{\bigstar\:\textsf{Solution :}}$

$\sf \bigg(x^2+x+1\bigg)= \bigg(x+\dfrac{1}{2}\bigg)^2+q^2$

$\\\\\hookrightarrow \sf \bigg(x^2+x+1\bigg)=\bigg(x\bigg)^2+\bigg(\dfrac{1}{2}\bigg)^2+\bigg(2 \times x \times \dfrac{1}{2}\bigg)+q^2\\\\\\\hookrightarrow \sf x^2+x+1 = x^2+ \dfrac{1}{4} +x + q^2\\\\\\\hookrightarrow \sf x^2 - x^2 + x - x + 1 - \frac{1}{4} =q^2\\\\\\\hookrightarrow \sf 1 - \dfrac{1}{4} =q^2\\\\\\\hookrightarrow \sf \dfrac{4 - 1}{4} =q^2\\\\\\\hookrightarrow \sf \dfrac{3}{4} =q^2\\\\\hookrightarrow \sf \sqrt{\dfrac{3}{4} } = q\\\\\\\hookrightarrow \underline{\boxed{\sf q = \pm\: \dfrac{ \sqrt{3} }{2}}}$

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