Question

xy হলে, দেখাও যে, x2 + y2
xy।
ii) 3x - 4y x​

Answer 1

Answer❀✿°᭄

(3x-4y) ∝√xy

Or, (3x-4y)=k√xy…(i)

Or,(3x-4y)^(2)=k^2×xy(squaring both sides)

Or,(3x+4y)^(2)-4xy=k’xy

(using (a-b)^2=(a+b)^2-4ab)

Or,(3x+4y)^(2)=xy(4+k’)

Or,(3x+4y)=k”√xy…(ii) (square rooting)

(i)+(ii)

9x=(k’+k”)√xy

Or,x=c√xy

Or, x^2=c’xy…(iii)

(ii)-(i)

8y=(k”-k’)√xy

Or,y=p√xy

Or,y^2=p’xy…(iv)

(iii)+(iv)

x^2+y^2=(c’+p’)xy

So, x^2+y^2 ∝xy

Hence proved.

[ here k, k’ , k” , c , c’ , p , p’ are constants]