Ratio and proportion.....

If x/a = y/b = z/c, prove that-

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Let x/a=y/b=z/c each equal to k.

Then x= ak,y=bl and z =ck. Substituting in {(a^2x^2-(b^2y^2+c^2y^2/(a^2x-b^2y+c^2)}#/2

= {[a^2(ak)^2-b^2(bk)^2+c^2(ck)^2]/[a^2a-kb^2bk+c^2ck]}(3/2)

={(a^3-b^3+c^3)k^2/ (a^3-b^3+c^3)k}^(3/2)

=k^(3/2) = (k^3)^(1/2), as x/a=y/b=z/c each equal to k.

= (xyz/abc)^(3/2) as

If x/a = y/b = z/c,

let x/a = y/b = z/c=k

we have,

putting above values in lhs then we have answer.

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