Question

if (x+y)varies as (x-y) and (y+z) varies as (y-z) then show that (x⁵+x²y³+yz⁴) varies as (x⁵+y⁵+z⁵)

pls solve it aasap​

Answer 1

Answer:

It is given that x, y, z are in A.P. Therefore, y−x=z−y=d(say)

Now, (x2+zx+z2)−(x2+xy+y2)=(−y2+z2)+x(z−y)=(z−y)(x+y+z)=d(x+y+z) 

and, (z2+yz+y2)−(z2+zx+x2)=(y2−x2)+z(y−x)=(y−x)(x+y+z)=d(x+y+z)

∴(x2+zx+z2)−(x2+xy+y2)=(z2+yz+y2)−(z2+zx+x2)

⇒x2+xy+y2,z2+zx+x