What is the answer to 1+\sqrt[4]{5x}=sqrt(5x) ?

The answer to 1+\sqrt[4]{5x}=sqrt(5x) is x=(7+3sqrt(5))/(10)

Solve for x: 1+\sqrt[4]{5x}=sqrt(5x)

The solution is x=(7+3sqrt(5))/(10)

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x = \frac{7 + 3 5}{10}

Decimal Notation

x = 1.37082 \dots

Solution steps

Use the following exponent property

Rewrite the equation with

1 + u = u^{2}

Solve

1 + u = u^{2} : u = \frac{1 + 5}{2}, u = \frac{1 - 5}{2}

u = \frac{1 + 5}{2}, u = \frac{1 - 5}{2}

Substitute back

solve for

x

Solve

No Solution for

x \in R

x = \frac{7 + 3 5}{10}

Verify Solutions:

x = \frac{7 + 3 5}{10}

True

The solution is

x = \frac{7 + 3 5}{10}

z^{2} + 8 z + 4 = z

x + 6 x - 23 = 5

x + 30 = x

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

2 x + 8 = x + 4

What is the answer to 1+\sqrt[4]{5x}=sqrt(5x) ?
The answer to 1+\sqrt[4]{5x}=sqrt(5x) is x=(7+3sqrt(5))/(10)
Solve for x: 1+\sqrt[4]{5x}=sqrt(5x)
The solution is x=(7+3sqrt(5))/(10)