What is the answer to 2(x-[ 1/x ])^2+3(x+[ 1/x ])-12=0 ?

The answer to 2(x-[ 1/x ])^2+3(x+[ 1/x ])-12=0 is x=2,x= 1/2 ,x=-2+sqrt(3),x=-2-sqrt(3)

Solve for x: 2(x-[ 1/x ])^2+3(x+[ 1/x ])-12=0

The solution is x=2,x= 1/2 ,x=-2+sqrt(3),x=-2-sqrt(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2 (x - [\frac{1}{x}])^{2} + 3 (x + [\frac{1}{x}]) - 12 = 0

x = 2, x = \frac{1}{2}, x = - 2 + 3, x = - 2 - 3

Decimal Notation

x = 2, x = 0.5, x = - 0.26794 \dots, x = - 3.73205 \dots

Solution steps

2 (x - [\frac{1}{x}])^{2} + 3 (x + [\frac{1}{x}]) - 12 = 0

Multiply by LCM

2 x^{4} + 3 x^{3} + 2 + 3 x - 16 x^{2} = 0

Solve

2 x^{4} + 3 x^{3} + 2 + 3 x - 16 x^{2} = 0 : x = 2, x = \frac{1}{2}, x = - 2 + 3, x = - 2 - 3

x = 2, x = \frac{1}{2}, x = - 2 + 3, x = - 2 - 3

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = 2, x = \frac{1}{2}, x = - 2 + 3, x = - 2 - 3

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

\frac{3.5}{x} = \frac{10.5}{6}

x \cdot x^{- 3} = \frac{27}{64}

(x + 2) \cdot (\frac{100}{x - 15}) = 100

\frac{1}{x} + 1 - \frac{1}{x} - 1 = 1

What is the answer to 2(x-[ 1/x ])^2+3(x+[ 1/x ])-12=0 ?
The answer to 2(x-[ 1/x ])^2+3(x+[ 1/x ])-12=0 is x=2,x= 1/2 ,x=-2+sqrt(3),x=-2-sqrt(3)
Solve for x: 2(x-[ 1/x ])^2+3(x+[ 1/x ])-12=0
The solution is x=2,x= 1/2 ,x=-2+sqrt(3),x=-2-sqrt(3)