Question

if 5(1/x^2+1/y^2+1/z^2)=4(1/xy+1/yz+1/zx) then find the value of 1/x+1/y+1/z

Answer 1

Answer:

Algebra,

We have,

5 \times (\frac{1}{ {x}^{2} } + \frac{1}{ {y}^{2} } + \frac{1}{ {z}^{2} } ) = 4 \times ( \frac{1}{xy} + \frac{1}{yz} + \frac{1}{xz} )5×(

x

2

1

+

y

2

1

+

z

2

1

)=4×(

xy

1

+

yz

1

+

xz

1

)

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,

\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \sqrt{\frac{14}{5} ( \frac{1}{xy} + \frac{1}{yz} + \frac{1}{xz})}

x

1

+

y

1

+

z

1

=

5

14

(

xy

1

+

yz

1

+

xz

1

)

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.

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