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

The answer to sqrt(x)-\sqrt[4]{x}=1 is x= 7/2+(3sqrt(5))/2

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

The solution is x= 7/2+(3sqrt(5))/2

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x = \frac{7}{2} + \frac{3 5}{2}

Decimal Notation

x = 6.85410 \dots

Solution steps

Use the following exponent property

Rewrite the equation with

u^{2} - u = 1

Solve

u^{2} - u = 1 : 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}{2} + \frac{3 5}{2}

Verify Solutions:

x = \frac{7}{2} + \frac{3 5}{2}

True

The solution is

x = \frac{7}{2} + \frac{3 5}{2}

w + 7 = 8

x + 20 - 5 x + 34 = 0

(x + 3)^{\frac{4}{3}} = 81

(5 x + 2)^{2} = 64

What is the answer to sqrt(x)-\sqrt[4]{x}=1 ?
The answer to sqrt(x)-\sqrt[4]{x}=1 is x= 7/2+(3sqrt(5))/2
Solve for x: sqrt(x)-\sqrt[4]{x}=1
The solution is x= 7/2+(3sqrt(5))/2