What is the answer to (x^2-4)^{3/2}=27 ?

The answer to (x^2-4)^{3/2}=27 is x=sqrt(13),x=-sqrt(13)

Solve for x: (x^2-4)^{3/2}=27

The solution is x=sqrt(13),x=-sqrt(13)

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(x^{2} - 4)^{\frac{3}{2}} = 27

x = 13, x = - 13

Decimal Notation

x = 3.60555 \dots, x = - 3.60555 \dots

Solution steps

(x^{2} - 4)^{\frac{3}{2}} = 27

Take both sides of the equation to the power of

2 : (x^{2} - 4)^{3} = 729

(x^{2} - 4)^{3} = 729

Solve

(x^{2} - 4)^{3} = 729 : x = 13, x = - 13

x = 13, x = - 13

Verify Solutions:

x = 13

True

, x = - 13

True

The solutions are

x = 13, x = - 13

20 x = 5 x

x - 1 = x

x^{\frac{1}{3}} = - 5

x^{\frac{1}{3}} = - 4

What is the answer to (x^2-4)^{3/2}=27 ?
The answer to (x^2-4)^{3/2}=27 is x=sqrt(13),x=-sqrt(13)
Solve for x: (x^2-4)^{3/2}=27
The solution is x=sqrt(13),x=-sqrt(13)