Home
Class 11
MATHS
If x^2+9y^2+25z^2=xyz(15/x+5/y+3/z) then...

If `x^2+9y^2+25z^2=xyz(15/x+5/y+3/z)` then x,y,z in

A

A.P.

B

G.P.

C

A.G.P.

D

H.P.

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`x^(2)+9y^(2)+25z^(2)=xyz((15)/(x)+(5)/(y)+(3)/(z))`
`rArr" "x^(2)+9y^(2)+25z^(2)-15yz-5xz-3xy=0`
`rArr" "(x^(2)-6xy+9y^(2))+(9y^(2)+25z^(2)-30yz)+(x^(2)-10xz+25z^(2))=0`
`rArr" "(x-3y)^(2)+(3y-5z)^(2)+(x-5z)^(2)=0`
`rArr" "x-3y=0,3y-5z=andx-5z=0`
`rArr" "x=3y=5z`
`rArr" "(x)/(1)=(y)/(1//3)=(z)/(1//5)=(1)/(lamda)" (say)"rArrx=(1)/(lamda),y=(1)/(3lamda),z=(1)/(5lamda)`
Clearly, x,y,z are in H.P.
Promotional Banner

Similar Questions

Explore conceptually related problems

If x^(2)+9y^(2)+35z62=xyz((15)/(x)+(5)/(y)+(3)/(z)) then x,y,z in

If x^(2)+9y^(2)+25z^(2)=xyz((15)/(x)+(5)/(y)+(3)/(z)), then x,y, andz are in H.P.(1)/(x),(1)/(y),(1)/(z) are in A.P.c.x,y,z are in G.P.d.(1)/(a)+(1)/(d)=(1)/(b)=(1)/(c)

If x,y,z are real numbers satisfying the equation 25(9x^2+y^2)+9z^2-15(5xy+yz+3zx)=0 then prove that x,y,z are in AP.

If 4 x^(2) + 9y^(2) + z^(2) + 49 = 12 ( x+ y + z) , then what is the value of (4x + 9y - z) ?

If (2x-y)^(2)+(3y-z)^(2)=0 then x:y:z is

If x,y,z are real and 4x^(2)+9y^(2)+16z^(2)=2xyz{(6)/(x)+(4)/(y)+(3)/(z)}

The product (2x-3y+5z)(4x^(2)+9y^(2)+25z^(2)+6xy+15yz-10xz) is

If x + y + z = 6 and x^2 + y^2 + z^2= 20 then the value of x^3 + y^3 + z^3 - 3xyz is

If x^(3)+y^(3)+z^(3)=3xyz and x+y+z=0 , then the value of ((x+y)^(2))/(xy)+((y+z)^(2))/(yz)+((z+x)^(2))/(zx) is