What is the answer to 4+2x=sqrt(12)+sqrt(1+x^2) ?

The answer to 4+2x=sqrt(12)+sqrt(1+x^2) is x=(-8+4sqrt(3)+sqrt(31-16\sqrt{3)})/3

Solve for x: 4+2x=sqrt(12)+sqrt(1+x^2)

The solution is x=(-8+4sqrt(3)+sqrt(31-16\sqrt{3)})/3

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4 + 2 x = 12 + 1 + x^{2}

x = \frac{- 8 + 4 3 + 31 - 16 3}{3}

Decimal Notation

x = 0.24708 \dots

Solution steps

4 + 2 x = 12 + 1 + x^{2}

Expand

12 + 1 + x^{2} : 23 + 1 + x^{2}

4 + 2 x = 23 + 1 + x^{2}

Remove square roots

4 x^{2} + 16 x - 83 x + 28 - 163 = 1 + x^{2}

Solve

4 x^{2} + 16 x - 83 x + 28 - 163 = 1 + x^{2} : x = \frac{- 8 + 4 3 + 31 - 16 3}{3}, x = \frac{- 8 + 4 3 - 31 - 16 3}{3}

x = \frac{- 8 + 4 3 + 31 - 16 3}{3}, x = \frac{- 8 + 4 3 - 31 - 16 3}{3}

Verify Solutions:

x = \frac{- 8 + 4 3 + 31 - 16 3}{3}

True

, x = \frac{- 8 + 4 3 - 31 - 16 3}{3}

False

The solution is

x = \frac{- 8 + 4 3 + 31 - 16 3}{3}

2 x^{\frac{5}{3}} - 6 = 0

x - 2 x + 1 = 2

x + 4 - x - 2 = 2

2 x - 7 x^{\frac{1}{2}} - 30 = 0

1 = 4 - (x - 3)^{2}

What is the answer to 4+2x=sqrt(12)+sqrt(1+x^2) ?
The answer to 4+2x=sqrt(12)+sqrt(1+x^2) is x=(-8+4sqrt(3)+sqrt(31-16\sqrt{3)})/3
Solve for x: 4+2x=sqrt(12)+sqrt(1+x^2)
The solution is x=(-8+4sqrt(3)+sqrt(31-16\sqrt{3)})/3