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

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

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

Solution

x^{3} - 2 x = x

Solution

x = 0, x = 3

Solution steps

x^{3} - 2 x = x

Square both sides:

x^{3} - 4 x^{3} x + 4 x = x

x^{3} - 4 x^{3} x + 4 x = x

Factor

x^{3} - 4 x^{3} x + 4 x : x (x^{2} - 4 x^{2} + 4)

x (x^{2} - 4 x^{2} + 4) = x

Move

x

to the left side

x^{3} - 4 x^{2} x + 3 x = 0

Factor

x^{3} - 4 x^{2} x + 3 x : x (x^{2} - 4 x^{2} + 3)

x (x^{2} - 4 x^{2} + 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{2} - 4 x^{2} + 3 = 0

Solve

x^{2} - 4 x^{2} + 3 = 0 : x = 3, x = - 3, x = 1, x = - 1

x = 0, x = 3, x = - 3, x = 1, x = - 1

Verify Solutions:

x = 0

True

, x = 3

True

, x = - 3

False

, x = 1

False

, x = - 1

False

The solutions are

x = 0, x = 3

Graph

Popular Examples

\sqrt[4]{3x^2+54}=x

4 3 x^{2} + 54 = x

solvefor y,x^{2/3}+y^{2/3}=2 solve for

y, x^{\frac{2}{3}} + y^{\frac{2}{3}} = 2

sqrt(2x)+3=sqrt(x-1)

2 x + 3 = x - 1

(3x-5)^{1/4}=2

(3 x - 5)^{\frac{1}{4}} = 2

solvefor y,x=sqrt(1-y)solve for

y, x = 1 - y

Frequently Asked Questions (FAQ)

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

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

Solution

Solution

Graph

Popular Examples

Frequently Asked Questions (FAQ)

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

Solve for x: sqrt(x^3)-2sqrt(x)=sqrt(x)