Question

If (1/x^3+1/y^3)varies as 1/(x^3+y^3) then prove that x varies as y

Answer 1

Step-by-step explanation:

1/x^3+ 1/y^3=k/(x^3 +y^3)

or,

(x^3+ y^3)/x^3 + (x^3+y^3)/y^3 -k=0

or,

1 + y^3/x^3 + x^3/y^3 +1 -k=0

or,

1+p+1/p +1-k=0 [ putting y^3/x^3 = p]

or,

(p^2 +1) /p +3 -k= 0

or,

p^2 +1+ 2p -kp= 0

or,

p^2 -(2+k) p+1 =0

so, p= (2+k) ± √{(2+k)^2 -4}/ 4 = constant= m (let constant be m)

so, y^3/ x^3 =k

or,

y/x = constant

so,

x veries y

[ proved ]