$\frac{1}{x}+\frac{x}{2}=5$

Willow Pratt
2022-06-30
Answered

Solve the following equations:

$\frac{1}{x}+\frac{x}{2}=5$

$\frac{1}{x}+\frac{x}{2}=5$

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Miles Mueller

Answered 2022-07-01
Author has **11** answers

$\frac{1}{x}+\frac{x}{2}=\frac{5}{1}$, A) Multiply by LCM

$LCM:2x$, B) Common Denominator

$2x(\frac{1}{x}+\frac{x}{2})=2x(5)$

$2+{x}^{2}=10x$

${x}^{2}-10x+2=0,a=1;b=-10;c=2$

$x=\frac{-b\pm \sqrt{{b}^{2}-4ac}}{2(1)}$

$=\frac{10\pm \sqrt{92}}{2}=\frac{10\pm \sqrt{4\ast 23}}{2}=\frac{10\pm 2\sqrt{23}}{2}=\frac{10}{2}\pm \frac{2\sqrt{23}}{2}=5\pm \sqrt{23}$

$LCM:2x$, B) Common Denominator

$2x(\frac{1}{x}+\frac{x}{2})=2x(5)$

$2+{x}^{2}=10x$

${x}^{2}-10x+2=0,a=1;b=-10;c=2$

$x=\frac{-b\pm \sqrt{{b}^{2}-4ac}}{2(1)}$

$=\frac{10\pm \sqrt{92}}{2}=\frac{10\pm \sqrt{4\ast 23}}{2}=\frac{10\pm 2\sqrt{23}}{2}=\frac{10}{2}\pm \frac{2\sqrt{23}}{2}=5\pm \sqrt{23}$

Jeffrey Jordon

Answered 2022-07-07
Author has **2581** answers

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