If x^2+9 y^2+25 z^2=x y z ( 15 x + 5 y + 3 z ) , the x, y, z are in

Step-by-step solution

aligned & x^2+9 y^2+25 z^2=15 y z+5 z x+3 x y & (x)^2+(3 y)^2+(5 z)^2-(x)(3 y)-(3 y)(5 z)-(x)(5 z)=0 & 1 2 [2(x)^2+2(3 y)^2+2(5 z)^2-2(x)(3 y)-2(3 y)(5 z)-2(x)(5 z) ] & = 1 2 [(x-3 y)^2+(3 y-5 z)^2+(x-5 z)^2 ]=0 & x-3 y=0,3 y-5 z=0, x-5 z=0 & 1 x = 1 3 y and 5 3 y = 1 z and 1 5 z = 1 x & 1 x + 1 z = 1 3 y + 5 3 y = 2 y aligned 1 x , 1 y , 1 z are in A.P. and x, y, z are in H.P.