tex]?Please answer with solution, thanks in advance! :))...

Questions

August 2022 1 8 Report

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! :))

Answers & Comments

suprathiksirimilla20

Answer:

A simple but fast and strong approach could be:

$\sf xyz=1 \implies \dfrac{1}{z} =xy$

Substitute this in the equation y+1/z=1/3.

$\sf y+xy=\dfrac{1}{3}$

$\sf y(1+x)=\dfrac{1}{3}$

$\sf y=\dfrac{1}{3(1+x)}$

Substitute this in maybe x + 1/y = 15

$\sf x + \dfrac{1}{\frac{1}{3(x+1)}}=15$

Solving this, x = 3.

Perfect! We got the value of x!

$\sf 3+\dfrac{1}{y} =15$

$\sf y =1/12$

Now,

$\sf xyz=1$

$\sf 3 \times \dfrac{1}{12} \times z=1$

$\sf z=4$

x + 1/z is 3+1/4 which is 3.25 or 13/4.

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#CarryOnLearning

xXSumanXx Marvellous answer :D

DeanGD20 Wonderful!

suprathiksirimilla20 tnx :D

AlbertEinstein351 Hi!
How are you?
Can you answer this question:
C. Solve graphically and find one possible solution for this problem.

Problem: It takes Mark 75 minutes and 3 cans of ...
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suprathiksirimilla20 Sure :D

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