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

Answer:

± √3/2  or  ± √(3/4)

Step-by-step explanation:

Since both are same, just written in other forms, we can say

⇒ x² + x + 1 = (x + 1/2)²  + q²

⇒ x² + x + 1 = x² + (1/2)² + 2(x)(1/2) + q²

⇒ x² + x + 1 = x² + 1/4 + x + q²

⇒ 1 = 1/4 + q²

⇒ 1 - 1/4 = q²

⇒ 3/4 = q²

⇒ ± √(3/4) = q   or  ± √3/2 = q

Answer 2

Answer:

$\underline{\bigstar\:\textsf{According to the given Question :}}$

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