Question

if x is proportion to y then show that x2=y2 proportional to xy​

Answer 1

Answer:

(x+y) is proportion to (x-y) .

Therefore, (x+y)=k.(x-y).

or , (x+y)^2 = k^2.(x-y)^2.

or , x^2+y^2+2xy = k^2.(x^2+y^2-2xy).

or. (x^2+y^2) -k^2.(x^2+y^2) = - 2xy -2.k^2.xy.

or, (x^2+y^2).(1-k^2) = -2.(1+k^2).xy.

or , (x^2+y^2) = {-2.(1+k^2)/(1-k^2)}.xy.

or , (x^2+y^2) = C. xy. , where constant C= {-2.(1+k^2)/(1-k^2)}.

Hence , x^2 +y^2 is proportion to xy.

 

Step-by-step explanation:

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