Let x, y, and z be three positive real numbers that satisfy the following system of equations:
[tex]xyz=1[/tex]
[tex]x + \frac{1}{y} =15[/tex]
[tex]y+\frac{1}{z}=\frac{1}{3}[/tex]
What is the value of [tex]z+\frac{1}{x}[/tex]?
Please answer with solution, thanks in advance! :))
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Answer:
A simple but fast and strong approach could be:
Substitute this in the equation y+1/z=1/3.
Substitute this in maybe x + 1/y = 15
Solving this, x = 3.
Perfect! We got the value of x!
Now,
x + 1/z is 3+1/4 which is 3.25 or 13/4.
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