Question

if (x^2+x+1) is written in the form (x+1/2)^2+q^2

Solve

Answer 1

Answer:

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:

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Explanation:

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