# Algebra

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

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

Note by Space Sizzlers
3 years, 7 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

- 3 years, 7 months ago

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

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

Staff - 3 years, 7 months ago

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

- 3 years, 7 months ago

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 $x = 1, y = 2$. I'm going to ask them to solve $x+y = 3$."

Staff - 3 years, 7 months ago

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

- 3 years, 7 months ago

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.

Staff - 3 years, 7 months ago

What have you tried? Where did you get stuck?

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

Staff - 3 years, 7 months ago

- 3 years, 7 months ago

You should begin by telling us what you have tried.

- 3 years, 7 months ago