What is the answer to sqrt(3\sqrt{x-3)}=3-sqrt(x) ?

The answer to sqrt(3\sqrt{x-3)}=3-sqrt(x) is x\approx 3.23209…

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sqrt(3\sqrt{x-3)}=3-sqrt(x)

3 x - 3 = 3 - x

x \approx 3.23209 \dots

Solution steps

3 x - 3 = 3 - x

Remove square roots

144 x^{3} + 2592 x^{2} + 11664 x = x^{4} + 90 x^{3} + 2241 x^{2} + 9720 x + 11664

Switch sides

x^{2} - 12 x x + 54 x - 108 x + 81 = 9 x - 27

Move

x^{2}

to the right side

- 12 x x + 54 x - 108 x + 81 = 9 x - 27 - x^{2}

Move

54 x

to the right side

- 12 x x - 108 x + 81 = - x^{2} - 45 x - 27

Move

81

to the right side

- 12 x x - 108 x = - x^{2} - 45 x - 108

Factor

- 12 x x - 108 x : - 12 x (x + 9)

- 12 x (x + 9) = - x^{2} - 45 x - 108

Solve

144 x^{3} + 2592 x^{2} + 11664 x = x^{4} + 90 x^{3} + 2241 x^{2} + 9720 x + 11664 : x \approx 3.23209 \dots, x \approx 60.30210 \dots

x \approx 3.23209 \dots, x \approx 60.30210 \dots

Verify Solutions:

x \approx 3.23209 \dots

True

, x \approx 60.30210 \dots

False

The solution is

x \approx 3.23209 \dots

x^{2} - 2 x - x = 0

- x = x

3 m^{\frac{3}{4}} + 7 = 12

19 - 3 x = x + 7

x (x - 15) - 4 = 0

What is the answer to sqrt(3\sqrt{x-3)}=3-sqrt(x) ?
The answer to sqrt(3\sqrt{x-3)}=3-sqrt(x) is x\approx 3.23209…
Solve for x: sqrt(3\sqrt{x-3)}=3-sqrt(x)
The solution is x\approx 3.23209…