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

The answer to sqrt(x)+x=sqrt(3x+x^2) is x=0,x=1

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sqrt(x)+x=sqrt(3x+x^2)

x + x = 3 x + x^{2}

x = 0, x = 1

Solution steps

x + x = 3 x + x^{2}

Square both sides:

x + 2 x x + x^{2} = 3 x + x^{2}

x + 2 x x + x^{2} = 3 x + x^{2}

Subtract

3 x + x^{2}

from both sides

x + 2 x x + x^{2} - (3 x + x^{2}) = 3 x + x^{2} - (3 x + x^{2})

Simplify

2 x x - 2 x = 0

Factor

2 x x - 2 x : 2 x (x - 1)

2 x (x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 1 = 0

Solve

x - 1 = 0 : x = 1

x = 0, x = 1

Verify Solutions:

x = 0

True

, x = 1

True

The solutions are

x = 0, x = 1

2 - x = 2 - 7 x

\frac{y}{4} = y - 3

x + 1 - 2 x - 5 - x - 2 = 0

2 x^{\frac{5}{2}} - 7 = 23

\frac{5 x - 6}{3 x ^{\frac{1}{3}}} = 0

What is the answer to sqrt(x)+x=sqrt(3x+x^2) ?
The answer to sqrt(x)+x=sqrt(3x+x^2) is x=0,x=1
Solve for x: sqrt(x)+x=sqrt(3x+x^2)
The solution is x=0,x=1