What is the answer to sqrt(x)+\sqrt[3]{x}=12 ?

The answer to sqrt(x)+\sqrt[3]{x}=12 is x=64

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sqrt(x)+\sqrt[3]{x}=12

x + 3 x = 12

x = 64

Solution steps

x + 3 x = 12

Use the following exponent property

: n a = (m a)^{\frac{m}{n}}

x = (3 x)^{\frac{3}{2}}

(3 x)^{\frac{3}{2}} + 3 x = 12

Rewrite the equation with

3 x = u

u^{\frac{3}{2}} + u = 12

Solve

u^{\frac{3}{2}} + u = 12 : u = 4

u = 4

Substitute back

u = 3 x,

solve for

x

Solve

3 x = 4 : x = 64

x = 64

Verify Solutions:

x = 64

True

The solution is

x = 64

y, x = y - 2

7 - x = x + 5

y, x = y - 4

2 x^{2} - 1 = x - 1

x + 3 = x + 1

What is the answer to sqrt(x)+\sqrt[3]{x}=12 ?
The answer to sqrt(x)+\sqrt[3]{x}=12 is x=64
Solve for x: sqrt(x)+\sqrt[3]{x}=12
The solution is x=64