Prove x2+y2+z2+w2=36 for Real Numbers x, y, z, w

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SUMMARY

The discussion centers on proving the equation x² + y² + z² + w² = 36 for real numbers x, y, z, and w, given the condition (x²/(n²-1)) + (y²/(n²-32)) + (z²/(n²-52)) + (w²/(n²-72)) = 1 for n = 2, 4, 6, and 8. Participants emphasize the importance of substituting the specified values of n to derive four equations with four unknowns, which is essential for solving the problem. The correct formulation of the equation is crucial for clarity and accuracy in the proof.

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jeedoubts
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Homework Statement


if the real numbers x,y,z,w satisfy (x2/(n2-1))+(y2/(n2-32))+(z2/(n2-52))+(w2/(n2-72)) for n=2,4,6,8 then prove
x2+y2+z2+w2=36

Homework Equations


The Attempt at a Solution


unable to think of anything?:confused:
 
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Unless I'm missing something, the problem you posted isn't consistent - what do your numbers x, y, z, w satisfy?
 
radou said:
Unless I'm missing something, the problem you posted isn't consistent - what do your numbers x, y, z, w satisfy?


sorry the exact equation is as follows
[(x2/(n2-1))+(y2/(n2-32))+(z2/(n2-52))+(w2/(n2-72))]=1
 
please help:confused::confused:
 
Edit: Add "= 1" to make an equation below.
jeedoubts said:

Homework Statement


if the real numbers x,y,z,w satisfy (x2/(n2-1))+(y2/(n2-32))+(z2/(n2-52))+(w2/(n2-72)) = 1 for n=2,4,6,8 then prove
x2+y2+z2+w2=36




Homework Equations





The Attempt at a Solution


unable to think of anything?:confused:
You're unable to think of anything? The most obvious starting point is substituting n = 2, n = 4, n = 6, and n = 8, and seeing what you get.
 
Mark44 said:
Edit: Add "= 1" to make an equation below.
You're unable to think of anything? The most obvious starting point is substituting n = 2, n = 4, n = 6, and n = 8, and seeing what you get.
That will give you four different equations in four unknowns -- in other words, exactly what is needed to solve the problem.
 

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