What is the answer to (x+1)^2=sqrt(7+4\sqrt{3x)} ?

The answer to (x+1)^2=sqrt(7+4\sqrt{3x)} is x\approx 0.92225…

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(x+1)^2=sqrt(7+4\sqrt{3x)}

(x + 1)^{2} = 7 + 4 3 x

x \approx 0.92225 \dots

Solution steps

(x + 1)^{2} = 7 + 4 3 x

Remove square roots

x^{8} + 8 x^{7} + 28 x^{6} + 56 x^{5} + 56 x^{4} - 56 x^{2} - 48 x + 36 = 48 x

Solve

x^{8} + 8 x^{7} + 28 x^{6} + 56 x^{5} + 56 x^{4} - 56 x^{2} - 48 x + 36 = 48 x : x \approx 0.32292 \dots, x \approx 0.92225 \dots

x \approx 0.32292 \dots, x \approx 0.92225 \dots

Verify Solutions:

x \approx 0.32292 \dots

False

, x \approx 0.92225 \dots

True

The solution is

x \approx 0.92225 \dots

x + 24 - x - 3 = 3

t, 3 t + 4 = - 6

x^{0.4} x - 3 = 2 x + 9

- 3 x + 4 = x

x = 3 + 3 - x

What is the answer to (x+1)^2=sqrt(7+4\sqrt{3x)} ?
The answer to (x+1)^2=sqrt(7+4\sqrt{3x)} is x\approx 0.92225…
Solve for x: (x+1)^2=sqrt(7+4\sqrt{3x)}
The solution is x\approx 0.92225…