Algebra

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

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

#Algebra

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

@Chew-Seong Cheong sir please help

space sizzlers - 4 years, 6 months ago

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

space sizzlers - 4 years, 6 months ago

You should begin by telling us what you have tried.

Jon Haussmann - 4 years, 6 months ago

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 - 4 years, 6 months ago

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

space sizzlers - 4 years, 6 months ago

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 - 4 years, 6 months ago

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

space sizzlers - 4 years, 6 months ago

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

Calvin Lin Staff - 4 years, 6 months ago

@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 - 4 years, 6 months ago

@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 - 4 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$