What is the answer to 3x^{16/5}-192x^2=0 ?

The answer to 3x^{16/5}-192x^2=0 is x=0,x=32,x=-32

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3x^{16/5}-192x^2=0

3 x^{\frac{16}{5}} - 192 x^{2} = 0

x = 0, x = 32, x = - 32

Solution steps

3 x^{\frac{16}{5}} - 192 x^{2} = 0

Use the following exponent property

: a^{\frac{n}{m}} = (a^{\frac{1}{m}})^{n}

x^{\frac{16}{5}} = (x^{\frac{1}{5}})^{16}

Use the following exponent property

: a^{n} = (a^{\frac{1}{m}})^{(n \cdot m)}

x^{2} = (x^{\frac{1}{5}})^{(2 \cdot 5)}

3 (x^{\frac{1}{5}})^{16} - 192 (x^{\frac{1}{5}})^{10} = 0

Rewrite the equation with

x^{\frac{1}{5}} = u

3 u^{16} - 192 u^{10} = 0

Solve

3 u^{16} - 192 u^{10} = 0 : u = 0, u = 2, u = - 2

u = 0, u = 2, u = - 2

Substitute back

u = x^{\frac{1}{5}},

solve for

x

Solve

x^{\frac{1}{5}} = 0 : x = 0

Solve

x^{\frac{1}{5}} = 2 : x = 32

Solve

x^{\frac{1}{5}} = - 2 : x = - 32

x = 0, x = 32, x = - 32

Verify Solutions:

x = 0

True

, x = 32

True

, x = - 32

True

The solutions are

x = 0, x = 32, x = - 32

x = 2 x

x + 10 - 1 = x

(2 a^{2} + 5 a + 2)^{\frac{1}{2}} = 3

2 x = x - 8

What is the answer to 3x^{16/5}-192x^2=0 ?
The answer to 3x^{16/5}-192x^2=0 is x=0,x=32,x=-32
Solve for x: 3x^{16/5}-192x^2=0
The solution is x=0,x=32,x=-32