if x/2 - 3/x = 5 what is x^2 / 4 + 9 / x^2?

Question

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1010

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if ${\frac{{\mathtt{x}}}{{\mathtt{2}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{3}}}{{\mathtt{x}}}} = {\mathtt{5}}$

what is ${\frac{{{\mathtt{x}}}^{{\mathtt{2}}}}{{\mathtt{4}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{9}}}{{{\mathtt{x}}}^{{\mathtt{2}}}}}$ ?

Guest Aug 13, 2015

+5

Best Answer

(x/2 - 3/x) ^2 = 5^2

X^2/4 - 3 + 9/x^2 = 25

X^2/4 + 9/x^2 = 25 + 3 = 28

Guest Aug 13, 2015

Guest · Answer 1 · 2015-08-13T03:02:28

(x/2 - 3/x) ^2 = 5^2

X^2/4 - 3 + 9/x^2 = 25

X^2/4 + 9/x^2 = 25 + 3 = 28

jdh3010 · Answer 2 · 2015-08-13T02:10:43

x/2-3/x=5

Multiply 2x to both sides

x^2-6=10x

Subtract 10x from both sides

x^2-10x-6=0

Add 6 to both sides

x^2-10x=6

→x(x-10)=6

x= ${\mathtt{5}}{\mathtt{\,\small\textbf+\,}}{\sqrt{{\mathtt{31}}}}$ or ${\mathtt{5}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{31}}}}$

So, x^2/4+9/x^2=28