1.

If 3 rational numbers x^(1//x) , y^(1//y) and z^(1//z) are equal and x^(yz)+y^(zx)+z^(xy)=729 , then find the value of x^(1//x)

Answer»

`6`
`3`
`5`
`4`

Solution :LET `x^(1//x)=y^(1//y)=z^(1//z)=k`
`:." "x=k^(x) , y=k^(y)andz=k^(z)`
`:." "x^(yz)=(k^(x))^(yz)=k^(xyz)`
`y^(zx)=(k^(y))^(zx)=k^(xyz)`
`z^(xy)=(k^(z))^(xy)=k^(xyz)`
`"Now , "x^(yz)+y^(zx)+z^(xy)=729`
`:." "k^(xyz)+k^(xyz)+k^(xyz)=729`
`rArr" "3*k^(xyz)=729`
`rArr" "k^(xyz)=243=(3)^(5)`
On comparison, we GET(because `k=x^(1//x)` is rational)
`rArr" "x^(1//x)=3`


Discussion

No Comment Found

Related InterviewSolutions