What is the answer to \sqrt[3]{x-2}+sqrt(x+1)=3 ?

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

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\sqrt[3]{x-2}+sqrt(x+1)=3

3 x - 2 + x + 1 = 3

x = 3

Solution steps

3 x - 2 + x + 1 = 3

Rewrite the equation with

3 x - 2 = u

and

x = u^{3} + 2

u + (u^{3} + 2) + 1 = 3

Solve

u + (u^{3} + 2) + 1 = 3 : u = 1

u = 1

Substitute back

u = 3 x - 2,

solve for

x

Solve

3 x - 2 = 1 : x = 3

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

x - 3 - x = 0

x + 2 = x - 4

x^{\frac{1}{2}} - 5 x^{\frac{1}{4}} + 4 = 0

x = 4 - x - 8

4 x + 7 = 2 x - 3 + 8

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