What is the answer to c*sqrt(x^2+x+1)=1 ?

The answer to c*sqrt(x^2+x+1)=1 is No Solution for x\in\mathbb{R}

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c*sqrt(x^2+x+1)=1

c \cdot x^{2} + x + 1 = 1

No Solution for x \in R

Solution steps

c x^{2} + x + 1 = 1

Divide both sides by

c

x^{2} + x + 1 = \frac{1}{c}

Square both sides:

x^{2} + x + 1 = \frac{1}{c ^{2}}

x^{2} + x + 1 = \frac{1}{c ^{2}}

Solve

x^{2} + x + 1 = \frac{1}{c ^{2}} : x = \frac{- c + - 3 c ^{2} + 4}{2 c}, x = - \frac{c + - 3 c ^{2} + 4}{2 c}

x = \frac{- c + - 3 c ^{2} + 4}{2 c}, x = - \frac{c + - 3 c ^{2} + 4}{2 c}

Verify Solutions:

x = \frac{- c + - 3 c ^{2} + 4}{2 c}

False

, x = - \frac{c + - 3 c ^{2} + 4}{2 c}

False

The solution is

No Solution for x \in R

x + x = 6

x + 6 = 5

x + 6 = 1

x, x + y + x + y = 30

9 x + 7 - x - 16 x - 7 = 0

What is the answer to c*sqrt(x^2+x+1)=1 ?
The answer to c*sqrt(x^2+x+1)=1 is No Solution for x\in\mathbb{R}