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Alexxandr [17]
3 years ago
8

Solve for x (1/x) -2/3 = (4x)

Mathematics
1 answer:
Vadim26 [7]3 years ago
4 0

The value of x is x=\frac{-1+\sqrt{37}}{12} and x=\frac{-1-\sqrt{37}}{12}

Step-by-step explanation:

The equation is \frac{1}{x}-\frac{2}{3}=4 x

Subtracting by 4x on both sides,

\frac{1}{x}-\frac{2}{3}-4 x=0

Taking LCM,

\frac{3-12 x^{2}-2 x}{3 x}=0

Multiplying by 3x on both sides,

-12 x^{2}-2 x+3=0

Dividing by (-) on both sides,

12 x^{2}+2 x-3=0

Using quadratic formula, we can solve for x.

\begin{aligned}x &=\frac{-2 \pm \sqrt{2^{2}-4 \cdot 12 \cdot(-3)}}{2 \cdot 12} \\&=\frac{-2 \pm \sqrt{4+144}}{2 \cdot 144} \\&=\frac{-2 \pm \sqrt{148}}{24} \\&=\frac{-2 \pm 2 \sqrt{37}}{24}\end{aligned}

Taking out common term 2, we get,

\begin{array}{l}{x=\frac{-2(1 \pm \sqrt{37})}{24}} \\{x=\frac{-1 \pm \sqrt{37}}{12}}\end{array}

Thus, the value of x is  x=\frac{-1+\sqrt{37}}{12} and x=\frac{-1-\sqrt{37}}{12}

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