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Asked by Maradana Rajesh kumar Last Modified
Answer 
Vivek Sharma
Atma Nand
Experienced (10+ Y) & Certified Mathematics Assistant Professor from Uttaranchal University, Dehradun
In this condition, there is no exact value given for the equation. Hence we cannot solve it without a given state. We cannot find a specific answer for each variable as there are no values given. I also tried the trial and error method, but the answer keeps fluctuating. We might have to create assumptions, and then we can solve it.
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5(x2 + y2 + z2) = 4(xy + yz + zx)
or, 5x2 + 5y2 + 5z2 = 4xy + 4yz + 4zx
or, 4x2 + 4y2 + 4z2 + x2 + y2 + z2 = 4xy + 4yz + 4zx
or, (4x2 – 4xy + y2) + (4y2 – 4yz + z2) + (4z2 – 4zx + x2) = 0
or, (2x - y)2 + (2y - z)2 + (2z - x)2 = 0
We know that, since sum of squares is 0, each square must be equal to 0.
Therefore,
(2x - y)2 = (2y - z)2 = (2z - x)2 = 0
or, (2x - y) = (2y - z) = (2z - x) = 0
Therefore,
2x = y, 2y = z, 2z = x.
Thus converting all terms in respect to ‘x’ we get,
y = 2x
z = x/2
Therefore,
x : y : z = x : 2x : x/2
= 1 : 2 : ½
= 2 : 4 : 1
Answer: x : y : z = 2 : 4 : 1
Susanta Kumar Mallick
Computer Professional Teacher with more than 15 years of experience in Computer Science
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