if x=a(b-c), y=b(a-b), z=c(a-b), then (x/a)^3+(y/b)^3+(z/c)^3 equal to
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x=a(b-c) 0r x/a = (b-c)……………..(1)
y =b(c-a) or y/b = (c-a)…………………(2)
z= =c(a-b) or z/c =(a-b)…………………….(3).
Prove that:-
(x/a)^3+(y/b)^3+(z/c)^3 = 3x.y.z/a.b.c.
L.H.S.
=(x/a)^3+(y/b)^3+(z/c)^3.
We have on adding eq.(1) ,(2) & (3).
x/a+y/b+z/c=b-c+c-a+a-b =0.
If x/a+y/b+z/c=0 then
(x/a)^3+(y/b)^3+(z/c)^3=3×(x/a)×(y/b)×(z/c).
or (x/a)^3+(y/b)^3+(z/c)^3 =3.x.y.z/a.b..c.
Proved.
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