Question

Use algebra to solve 3x+4 = 1/x
The exact solutions are x=
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Answer 1

Ignore the A before the ±, it wouldn't let me type it correctly.

`x=(2±√(7) )/(3)`

Explanation:

3x + 4 = 1 ÷ x

3x + 4 - 4 = 1 ÷ x - 4

3x = 1 ÷ x - 4

`3x=(1)/(x) +(x(-4))/(x)`

`3x=(1+x(-4))/(x)`

`3x=(1-4x)/(x)`

`x(3x)=x((1-4x)/(x))`

x · 3x = - 4x + 1

3x² = - 4x + 1

3x² - (- 4x + 1) = 0

3x² + 4x - 1 = 0

Ignore the A before the ±, it wouldn't let me type it correctly.

`x=\frac{-b±\sqrt{b^(2)-4ac } }{2a}`

a = 3

b = 4

c = - 1

`x=\frac{-4±\sqrt{4^(2)-4((3)(-1)) } }{2(3)}`

`x=(-4±√(16-4((3)(-1)) ) )/(2(3))`

`x=(-4±√(16+12 ) )/(2(3))`

`x=(-4±√(28 ) )/(2(3))`

`x=(-4±√((2)(14) ) )/(2(3))`

`x=(-4±√((2)(2)(7) ) )/(2(3))`

`x=(-4±√(2 ) √(2)√(7) )/(2(3))`

`x=(-4±2√(7) )/(2(3))`

`x=(-4±2√(7) )/(6)`

Two separate equations

`x=(-4+2√(7) )/(6)`

`x=(2+√(7) )/(3)`

`x=(-4-2√(7) )/(6)`

`x=(2-√(7) )/(3)`