Algebra

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

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

Note by Space Sizzlers
2 years, 10 months ago

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@Chew-Seong Cheong sir please help

space sizzlers - 2 years, 10 months ago

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

space sizzlers - 2 years, 10 months ago

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You should begin by telling us what you have tried.

Jon Haussmann - 2 years, 10 months ago

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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.

Calvin Lin Staff - 2 years, 10 months ago

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

space sizzlers - 2 years, 10 months ago

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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?

Calvin Lin Staff - 2 years, 10 months ago

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

space sizzlers - 2 years, 10 months ago

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@Space Sizzlers That is a very different question from what you asked. Which question are you wanting help with?

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

Calvin Lin Staff - 2 years, 10 months ago

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@Calvin Lin yes sir , i understand what you mean to say , but i could think of no other way , could you suggest an alternative approach

space sizzlers - 2 years, 10 months ago

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@Space Sizzlers So, for this problem, what have you tried? where did you get stuck? What else seems familiar? What other things can you try?

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.

Calvin Lin Staff - 2 years, 10 months ago

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