What is the answer to 9/x =(4-sqrt(x))^2 ?

The answer to 9/x =(4-sqrt(x))^2 is x=1,x=9,x=11+4sqrt(7)

Solve for x: 9/x =(4-sqrt(x))^2

The solution is x=1,x=9,x=11+4sqrt(7)

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\frac{9}{x} = (4 - x)^{2}

x = 1, x = 9, x = 11 + 47

Solution steps

\frac{9}{x} = (4 - x)^{2}

Multiply both sides by

x

\frac{9}{x} x = (4 - x)^{2} x

Simplify

9 = (4 - x)^{2} x

Expand

(4 - x)^{2} x : 16 x - 8 x x + x^{2}

9 = 16 x - 8 x x + x^{2}

Remove square roots

x^{4} + 32 x^{3} + 238 x^{2} - 288 x + 81 = 64 x^{3}

Solve

x^{4} + 32 x^{3} + 238 x^{2} - 288 x + 81 = 64 x^{3} : x = 1, x = 9, x = 11 + 47, x = 11 - 47

x = 1, x = 9, x = 11 + 47, x = 11 - 47

Verify Solutions:

x = 1

True

, x = 9

True

, x = 11 + 47

True

, x = 11 - 47

False

The solutions are

x = 1, x = 9, x = 11 + 47

2 x = 2 x - 4

1 = x^{\frac{3}{2}}

(x^{2} + 5) (x + 2) = x

x^{5} + x^{2} = π

7 t + 2 = - 4

What is the answer to 9/x =(4-sqrt(x))^2 ?
The answer to 9/x =(4-sqrt(x))^2 is x=1,x=9,x=11+4sqrt(7)
Solve for x: 9/x =(4-sqrt(x))^2
The solution is x=1,x=9,x=11+4sqrt(7)