Question

If 2x^ 2 +3y^ 2 propto xy , prove that +9x^ 4 +4y^ 4 propto x^ 2 y^ 2​

Answer 1

Step-by-step explanation:

(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]

If x2+xy+y2=a2x2+xy+y2=a2 , how will you prove that d2ydx2+6a2(x+2y)3=0d2ydx2+6a2(x+2y)3=0?

How do you prove x^2+y^2∝ xy, if (x+y) ∝(x-y)?

If f(x)=(x+33)2+(3343x+43)2−−−−−−−−−−−−−−−−−−−−√f(x)=(x+33)2+(3343x+43)2, how do I prove f(x)≥53f(x)≥53?

Answer 2

yes of course! you can tell me,who knows I may help you with that problem

I'm busy with online meetings

have a good day!