What is the answer to sqrt(10+\sqrt{3x)}=2+sqrt(6) ?

The answer to sqrt(10+\sqrt{3x)}=2+sqrt(6) is x=32

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sqrt(10+\sqrt{3x)}=2+sqrt(6)

10 + 3 x = 2 + 6

x = 32

Solution steps

10 + 3 x = 2 + 6

Square both sides:

10 + 3 x = 10 + 46

10 + 3 x = 10 + 46

Subtract

10

from both sides

10 + 3 x - 10 = 10 + 46 - 10

Simplify

3 x = 46

Square both sides:

3 x = 96

3 x = 96

Solve

3 x = 96 : x = 32

x = 32

Verify Solutions:

x = 32

True

The solution is

x = 32

y, x = 3 + - 4 - 2 y

x^{\frac{3}{2}} = 512

2 x = x 9 - x^{2}

2 x + 3 = 2 x + 3

- 2 x + 2 = 1 - x

What is the answer to sqrt(10+\sqrt{3x)}=2+sqrt(6) ?
The answer to sqrt(10+\sqrt{3x)}=2+sqrt(6) is x=32
Solve for x: sqrt(10+\sqrt{3x)}=2+sqrt(6)
The solution is x=32