What is the answer to sqrt(3x)-sqrt(x)-sqrt(2)=0 ?

The answer to sqrt(3x)-sqrt(x)-sqrt(2)=0 is x=2+sqrt(3)

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sqrt(3x)-sqrt(x)-sqrt(2)=0

3 x - x - 2 = 0

x = 2 + 3

Decimal Notation

x = 3.73205 \dots

Solution steps

3 x - x - 2 = 0

Remove square roots

4 x^{2} - 8 x + 4 = 8 x

Solve

4 x^{2} - 8 x + 4 = 8 x : x = 2 + 3, x = 2 - 3

x = 2 + 3, x = 2 - 3

Verify Solutions:

x = 2 + 3

True

, x = 2 - 3

False

The solution is

x = 2 + 3

2 x - 3 = 11

7 x + 58 = x + 10

x + 37 + 8 = 14

3 x - 8 = 1 + x + 1

8 x - 4 = x + 1

What is the answer to sqrt(3x)-sqrt(x)-sqrt(2)=0 ?
The answer to sqrt(3x)-sqrt(x)-sqrt(2)=0 is x=2+sqrt(3)
Solve for x: sqrt(3x)-sqrt(x)-sqrt(2)=0
The solution is x=2+sqrt(3)