5(1/x2+1/y2+1/z^2)=4(1/xy+1/yz+1/zx)
Then find out 1/x+1/y+1/z.
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Algebra,
We have,
1/x²+ 1/y²+ 1/z²= 4/5(1/xy + 1/yz + 1/xz)
(1/x + 1/y + 1/z)²-2(1/xy + 1/yz + 1/xz) = 4/5(1/xy + 1/yz + 1/xz)
(1/x + 1/y + 1/z)²=4/5(1/xy + 1/yz + 1/xz) + 2(1/xy + 1/yz + 1/xz)
(1/x + 1/y + 1/z)²=14/5(1/xy + 1/yz + 1/xz)
so the ansewr is,
or, 1/x + 1/y + 1/z = 1/xyz√{14/5(xy + yz + xz)}
I think it's the correct, infact sure it's the answer.
That's it
Hope it helped (・ิω・ิ)
We have,
1/x²+ 1/y²+ 1/z²= 4/5(1/xy + 1/yz + 1/xz)
(1/x + 1/y + 1/z)²-2(1/xy + 1/yz + 1/xz) = 4/5(1/xy + 1/yz + 1/xz)
(1/x + 1/y + 1/z)²=4/5(1/xy + 1/yz + 1/xz) + 2(1/xy + 1/yz + 1/xz)
(1/x + 1/y + 1/z)²=14/5(1/xy + 1/yz + 1/xz)
so the ansewr is,
or, 1/x + 1/y + 1/z = 1/xyz√{14/5(xy + yz + xz)}
I think it's the correct, infact sure it's the answer.
That's it
Hope it helped (・ิω・ิ)
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