Question

If (x + y) varies directly as (x - y), then (x² + y²) will
vary as
(A) x² - y²
(B) xy
(C) Both (A) and (B)
(D) None of these
Please explain on paper ​

Answer 1

Answer:

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

Answer 2

Given:

(x + y) varies directly as (x - y).

To find:

Find the $(x^{2} +y^{2} )$ values.

Step-by-step explanation:

$(x+y)=(x-y)$

$(x+y)(x-y)=0$

$x^{2} -xy+xy-y^{2} =0$

$(x^{2} -y^{2} )=0$

$(x-y)^{2} =0$

$x^{2} +y^{2} =2xy$

It means that,$x^{2} +y^{2}$ varies as $xy$.