Find the number of real solutions \((x,y,z,w)\) of the equation below.

\[ x+y+z+w = 11\left(\dfrac{1}{x} + \dfrac{1}{y} +\dfrac{1}{z} +\dfrac{1}{w}\right) \]

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## Comments

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TopNewest@Chew-Seong Cheong sir please help

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@Pi Han Goh@Calvin Lin@Jon Haussmann@Brian Charlesworth

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You should begin by telling us what you have tried.

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What have you tried? Where did you get stuck?

Simply demanding that others "do for me" isn't being respectful of them.

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i tried to take lcm and simplify but nothing helped that way......i do not know where to begin with

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Why would you expect there to be a "nicer" answer?

Are you sure you want real solutions instead of just integer solutions?

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sir i just added an image .....hope it helps question 15

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It's like saying "The original problem is solve for \( x = 1, y = 2 \). I'm going to ask them to solve \( x+y = 3 \)."

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E.g. I tried to combine all 4 equations. The larger equation cannot be easily solved. There seem to be a lot of solutions to this equation.

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