Question

If `(x)/(a)=(y)/(b)=(z)/(c)`, then prove that each ratio is equal to `((3x^(3)-11y^(3)+13z^(3))/(3a^(3)-11b^(3)+13c^(3)))^((1)/(3))`

Answer 1

Lwet `(x)/(a)=(y)/(b)=(z)/(c)=k`
`impliesx=ak,y=bk and z=ck`
`therefore((3x^(3)-11y^(3)+13z^(3))/(3a^(3)-11b^(3)+13c^(3)))^((1)/(3))=((3(ak)^(3)-11(bk)^(3)+13(ck)^(3))/(3a^(3)-11b^(3)+13c^(3)))^((1)/(3))=((k^(3)(3a^(3)-11b^(3)+13c^(3)))/((3a^(3)-11b^(3)+13c^(3))))^((1)/(3))=k` Hence, proved.