What is the answer to 2x^2+x+1-2sqrt(x^2+x+1)=0 ?

The answer to 2x^2+x+1-2sqrt(x^2+x+1)=0 is x=-1,x\approx 0.81718…

Solve for x: 2x^2+x+1-2sqrt(x^2+x+1)=0

The solution is x=-1,x\approx 0.81718…

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2 x^{2} + x + 1 - 2 x^{2} + x + 1 = 0

x = - 1, x \approx 0.81718 \dots

Solution steps

2 x^{2} + x + 1 - 2 x^{2} + x + 1 = 0

Remove square roots

4 x^{2} + 4 x + 4 = 4 x^{4} + 4 x^{3} + 5 x^{2} + 2 x + 1

Solve

4 x^{2} + 4 x + 4 = 4 x^{4} + 4 x^{3} + 5 x^{2} + 2 x + 1 : x = - 1, x \approx 0.81718 \dots

x = - 1, x \approx 0.81718 \dots

Verify Solutions:

x = - 1

True

, x \approx 0.81718 \dots

True

The solutions are

x = - 1, x \approx 0.81718 \dots

x^{0.5} = x

- 4 = 1 - x^{2} - 11

9 = 5 x - 4

2 x - 5 - 2 x = 0

2 (x + 15) - 3 = x

What is the answer to 2x^2+x+1-2sqrt(x^2+x+1)=0 ?
The answer to 2x^2+x+1-2sqrt(x^2+x+1)=0 is x=-1,x\approx 0.81718…
Solve for x: 2x^2+x+1-2sqrt(x^2+x+1)=0
The solution is x=-1,x\approx 0.81718…