What is the answer to x=2+sqrt(3)sqrt(x)+1sqrt(x) ?

The answer to x=2+sqrt(3)sqrt(x)+1sqrt(x) is x=2sqrt(9-4\sqrt{3)}+sqrt(3)sqrt(9-4\sqrt{3)}+4+sqrt(3)

Solve for x: x=2+sqrt(3)sqrt(x)+1sqrt(x)

The solution is x=2sqrt(9-4\sqrt{3)}+sqrt(3)sqrt(9-4\sqrt{3)}+4+sqrt(3)

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x = 2 + 3 x + 1 x

x = 2 9 - 43 + 3 9 - 43 + 4 + 3

Decimal Notation

x = 11.10386 \dots

Solution steps

x = 2 + 3 x + 1 \cdot x

Expand

2 + 3 x + 1 \cdot x : 2 + 3 x + x

x = 2 + 3 x + x

Switch sides

2 + 3 x + x = x

Move

2

to the right side

3 x + x = x - 2

Factor

3 x + x : (3 + 1) x

(3 + 1) x = x - 2

Divide both sides by

3 + 1

x = \frac{( 3 - 1 ) ( x - 2 )}{2}

Square both sides:

x = x^{2} - \frac{3 x ^{2}}{2} + 23 x - 4 x + 4 - 23

x = x^{2} - \frac{3 x ^{2}}{2} + 23 x - 4 x + 4 - 23

Solve

x = x^{2} - \frac{3 x ^{2}}{2} + 23 x - 4 x + 4 - 23 : x = 2 9 - 43 + 3 9 - 43 + 4 + 3, x = - 2 9 - 43 - 3 9 - 43 + 4 + 3

x = 2 9 - 43 + 3 9 - 43 + 4 + 3, x = - 2 9 - 43 - 3 9 - 43 + 4 + 3

Verify Solutions:

x = 2 9 - 43 + 3 9 - 43 + 4 + 3

True

, x = - 2 9 - 43 - 3 9 - 43 + 4 + 3

False

The solution is

x = 2 9 - 43 + 3 9 - 43 + 4 + 3

x^{\frac{3}{2}} = 12

4 - 3 x - 2 36 - 27 x + 5 = 0

\frac{- 1}{5 - \frac{1}{3} \cdot x + 1} = - \frac{17}{10}

x, 20 g \cdot x^{3} - 9^{2} = 2

x - 2 = - 2 x + 14

What is the answer to x=2+sqrt(3)sqrt(x)+1sqrt(x) ?
The answer to x=2+sqrt(3)sqrt(x)+1sqrt(x) is x=2sqrt(9-4\sqrt{3)}+sqrt(3)sqrt(9-4\sqrt{3)}+4+sqrt(3)
Solve for x: x=2+sqrt(3)sqrt(x)+1sqrt(x)
The solution is x=2sqrt(9-4\sqrt{3)}+sqrt(3)sqrt(9-4\sqrt{3)}+4+sqrt(3)