Question

(i) if x^2 + 5y^2 varies as 3xy, then prove that x^4+ y^4 varies as x^3y​

Answer 1

Step-by-step explanation:

Let x=ky then,

x

2

+y

2

=k

2

y

2

+y

2

=y

2

(k

2

+1)

x

2

−y

2

=k

2

y

2

−y

2

=y

2

(k

2

−1)

So

x

2

−y

2

x

2

+y

2

=

(k

2

−1)

(k

2

+1)

x

2

+y

2

=l(x

2

−y

2

) where l=

(k

2

−1)

(k

2

+1)

, a constant.

Answer 2

Answer:

(i) if x^2 + 5y^2 varies as 3xy, then prove that x^4+ y^4 varies as x^3y