What is the answer to x^{4/3}-5x^{2/3}+6=0 ?

The answer to x^{4/3}-5x^{2/3}+6=0 is x=3*3^{1/2},x=-3*3^{1/2},x=2*2^{1/2},x=-2*2^{1/2}

Solve for x: x^{4/3}-5x^{2/3}+6=0

The solution is x=3*3^{1/2},x=-3*3^{1/2},x=2*2^{1/2},x=-2*2^{1/2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^{\frac{4}{3}} - 5 x^{\frac{2}{3}} + 6 = 0

x = 3 \cdot 3^{\frac{1}{2}}, x = - 3 \cdot 3^{\frac{1}{2}}, x = 2 \cdot 2^{\frac{1}{2}}, x = - 2 \cdot 2^{\frac{1}{2}}

Decimal Notation

x = 5.19615 \dots, x = - 5.19615 \dots, x = 2.82842 \dots, x = - 2.82842 \dots

Solution steps

x^{\frac{4}{3}} - 5 x^{\frac{2}{3}} + 6 = 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}

(x^{\frac{1}{3}})^{4} - 5 (x^{\frac{1}{3}})^{2} + 6 = 0

Rewrite the equation with

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

u^{4} - 5 u^{2} + 6 = 0

Solve

u^{4} - 5 u^{2} + 6 = 0 : u = 3, u = - 3, u = 2, u = - 2

u = 3, u = - 3, u = 2, u = - 2

Substitute back

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

solve for

x

Solve

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

Solve

x^{\frac{1}{3}} = - 3 : x = - 3 \cdot 3^{\frac{1}{2}}

Solve

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

Solve

x^{\frac{1}{3}} = - 2 : x = - 2 \cdot 2^{\frac{1}{2}}

x = 3 \cdot 3^{\frac{1}{2}}, x = - 3 \cdot 3^{\frac{1}{2}}, x = 2 \cdot 2^{\frac{1}{2}}, x = - 2 \cdot 2^{\frac{1}{2}}

Verify Solutions:

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

True

, x = - 3 \cdot 3^{\frac{1}{2}}

True

, x = 2 \cdot 2^{\frac{1}{2}}

True

, x = - 2 \cdot 2^{\frac{1}{2}}

True

The solutions are

x = 3 \cdot 3^{\frac{1}{2}}, x = - 3 \cdot 3^{\frac{1}{2}}, x = 2 \cdot 2^{\frac{1}{2}}, x = - 2 \cdot 2^{\frac{1}{2}}

x + 20 + 2 x = 2

- 10 x - 10 = - 60

x + 3 = 2 x + 21

4 + x - 1 = x + 3

2 + x = x

What is the answer to x^{4/3}-5x^{2/3}+6=0 ?
The answer to x^{4/3}-5x^{2/3}+6=0 is x=3*3^{1/2},x=-3*3^{1/2},x=2*2^{1/2},x=-2*2^{1/2}
Solve for x: x^{4/3}-5x^{2/3}+6=0
The solution is x=3*3^{1/2},x=-3*3^{1/2},x=2*2^{1/2},x=-2*2^{1/2}