What is the answer to (x^2-5x-28)^{4/3}=16 ?

The answer to (x^2-5x-28)^{4/3}=16 is x=9,x=-4,x=(5+105^{1/2})/2 ,x=(5-105^{1/2})/2

Solve for x: (x^2-5x-28)^{4/3}=16

The solution is x=9,x=-4,x=(5+105^{1/2})/2 ,x=(5-105^{1/2})/2

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(x^{2} - 5 x - 28)^{\frac{4}{3}} = 16

x = 9, x = - 4, x = \frac{5 + 10 5 ^{\frac{1}{2}}}{2}, x = \frac{5 - 10 5 ^{\frac{1}{2}}}{2}

Solution steps

(x^{2} - 5 x - 28)^{\frac{4}{3}} = 16

Take both sides of the equation to the power of

3 : (x^{2} - 5 x - 28)^{4} = 4096

(x^{2} - 5 x - 28)^{4} = 4096

Solve

(x^{2} - 5 x - 28)^{4} = 4096 : x = 9, x = - 4, x = \frac{5 + 10 5 ^{\frac{1}{2}}}{2}, x = \frac{5 - 10 5 ^{\frac{1}{2}}}{2}

x = 9, x = - 4, x = \frac{5 + 10 5 ^{\frac{1}{2}}}{2}, x = \frac{5 - 10 5 ^{\frac{1}{2}}}{2}

Verify Solutions:

x = 9

True

, x = - 4

True

, x = \frac{5 + 10 5 ^{\frac{1}{2}}}{2}

True

, x = \frac{5 - 10 5 ^{\frac{1}{2}}}{2}

True

The solutions are

x = 9, x = - 4, x = \frac{5 + 10 5 ^{\frac{1}{2}}}{2}, x = \frac{5 - 10 5 ^{\frac{1}{2}}}{2}

x^{2} - 5 = 1 + x^{2}

x + 28 - x - 4 = 4

2 x - \frac{54}{x} = 0

3 t + 6 = - 6

x^{\frac{5}{7}} = 243

What is the answer to (x^2-5x-28)^{4/3}=16 ?
The answer to (x^2-5x-28)^{4/3}=16 is x=9,x=-4,x=(5+105^{1/2})/2 ,x=(5-105^{1/2})/2
Solve for x: (x^2-5x-28)^{4/3}=16
The solution is x=9,x=-4,x=(5+105^{1/2})/2 ,x=(5-105^{1/2})/2