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

The answer to sqrt(x^2-3)-sqrt(x)=3 is x\approx 5.64882…

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

x^{2} - 3 - x = 3

x \approx 5.64882 \dots

Solution steps

x^{2} - 3 - x = 3

Remove square roots

x^{4} - 2 x^{3} - 23 x^{2} + 24 x + 144 = 36 x

Solve

x^{4} - 2 x^{3} - 23 x^{2} + 24 x + 144 = 36 x : x \approx 5.64882 \dots, x \approx 2.28392 \dots

x \approx 5.64882 \dots, x \approx 2.28392 \dots

Verify Solutions:

x \approx 5.64882 \dots

True

, x \approx 2.28392 \dots

False

The solution is

x \approx 5.64882 \dots

2 x + 5 = - x + 5

x, 2 = x + y

x, (x + y)^{3} = 27

(1 - y^{2})^{\frac{1}{2}} = 0

x + 4 - 7 = 0

What is the answer to sqrt(x^2-3)-sqrt(x)=3 ?
The answer to sqrt(x^2-3)-sqrt(x)=3 is x\approx 5.64882…
Solve for x: sqrt(x^2-3)-sqrt(x)=3
The solution is x\approx 5.64882…