Question

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

Answer:

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

$x=\frac{2±\sqrt{7} }{3}$

Step-by-step explanation:

3x + 4 = 1 ÷ x

3x + 4 - 4 = 1 ÷ x - 4

3x = 1 ÷ x - 4

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

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

$3x=\frac{1-4x}{x}$

$x(3x)=x(\frac{1-4x}{x})$

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

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

$x=\frac{-4±\sqrt{16-4((3)(-1)) } }{2(3)}$

$x=\frac{-4±\sqrt{16+12 } }{2(3)}$

$x=\frac{-4±\sqrt{28 } }{2(3)}$

$x=\frac{-4±\sqrt{(2)(14) } }{2(3)}$

$x=\frac{-4±\sqrt{(2)(2)(7) } }{2(3)}$

$x=\frac{-4±\sqrt{2 } \sqrt{2}\sqrt{7} }{2(3)}$

$x=\frac{-4±2\sqrt{7} }{2(3)}$

$x=\frac{-4±2\sqrt{7} }{6}$

Two separate equations

$x=\frac{-4+2\sqrt{7} }{6}$

$x=\frac{2+\sqrt{7} }{3}$

$x=\frac{-4-2\sqrt{7} }{6}$

$x=\frac{2-\sqrt{7} }{3}$