What is the answer to 9x^{4/3}-10x^{2/3}+1=0 ?

The answer to 9x^{4/3}-10x^{2/3}+1=0 is x=1,x=-1,x= 1/27 ,x=-1/27

Solve for x: 9x^{4/3}-10x^{2/3}+1=0

The solution is x=1,x=-1,x= 1/27 ,x=-1/27

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9 x^{\frac{4}{3}} - 10 x^{\frac{2}{3}} + 1 = 0

x = 1, x = - 1, x = \frac{1}{27}, x = - \frac{1}{27}

Decimal Notation

x = 1, x = - 1, x = 0.03703 \dots, x = - 0.03703 \dots

Solution steps

9 x^{\frac{4}{3}} - 10 x^{\frac{2}{3}} + 1 = 0

Use the following exponent property

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

x^{\frac{4}{3}} = (x^{\frac{1}{3}})^{4}, x^{\frac{2}{3}} = (x^{\frac{1}{3}})^{2}

9 (x^{\frac{1}{3}})^{4} - 10 (x^{\frac{1}{3}})^{2} + 1 = 0

Rewrite the equation with

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

9 u^{4} - 10 u^{2} + 1 = 0

Solve

9 u^{4} - 10 u^{2} + 1 = 0 : u = 1, u = - 1, u = \frac{1}{3}, u = - \frac{1}{3}

u = 1, u = - 1, u = \frac{1}{3}, u = - \frac{1}{3}

Substitute back

u = x^{\frac{1}{3}},

solve for

x

Solve

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

Solve

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

Solve

x^{\frac{1}{3}} = \frac{1}{3} : x = \frac{1}{27}

Solve

x^{\frac{1}{3}} = - \frac{1}{3} : x = - \frac{1}{27}

x = 1, x = - 1, x = \frac{1}{27}, x = - \frac{1}{27}

Verify Solutions:

x = 1

True

, x = - 1

True

, x = \frac{1}{27}

True

, x = - \frac{1}{27}

True

The solutions are

x = 1, x = - 1, x = \frac{1}{27}, x = - \frac{1}{27}

(x^{2} + 1)^{2} = 5

x + x = 5

- 72 + 17 x = x

- 14 x + 2 = x - 3

y, 2 (x - 3)^{2} + (y - 2)^{2} = x^{2}

What is the answer to 9x^{4/3}-10x^{2/3}+1=0 ?
The answer to 9x^{4/3}-10x^{2/3}+1=0 is x=1,x=-1,x= 1/27 ,x=-1/27
Solve for x: 9x^{4/3}-10x^{2/3}+1=0
The solution is x=1,x=-1,x= 1/27 ,x=-1/27