What is the answer to x^2-5=sqrt(3x) ?

The answer to x^2-5=sqrt(3x) is x\approx 2.81143…

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x^2-5=sqrt(3x)

x^{2} - 5 = 3 x

x \approx 2.81143 \dots

Solution steps

x^{2} - 5 = 3 x

Square both sides:

x^{4} - 10 x^{2} + 25 = 3 x

x^{4} - 10 x^{2} + 25 = 3 x

Solve

x^{4} - 10 x^{2} + 25 = 3 x : x \approx 2.81143 \dots, x \approx 1.66320 \dots

x \approx 2.81143 \dots, x \approx 1.66320 \dots

Verify Solutions:

x \approx 2.81143 \dots

True

, x \approx 1.66320 \dots

False

The solution is

x \approx 2.81143 \dots

3 x^{\frac{16}{5}} - 192 x^{2} = 0

x = 2 x

x + 10 - 1 = x

(2 a^{2} + 5 a + 2)^{\frac{1}{2}} = 3

What is the answer to x^2-5=sqrt(3x) ?
The answer to x^2-5=sqrt(3x) is x\approx 2.81143…
Solve for x: x^2-5=sqrt(3x)
The solution is x\approx 2.81143…