Paragraph: If p = X - Y , q =X + Y and p ^2+4 pq + q ^2=A X^2+B Y^2, 0 0 2 Question: What is the value of A?

Step-by-step solution

aligned & p = x - y & q = x + y & Given, p ^2+4 p q+ q ^2=A x^2+B y^2 aligned Let us take = 4 . aligned & p=x 4 -y 4 = x-y 2 & q=x 4 +y 4 = x+y 2 & p q= x^2-y^2 2 2 p q=x^2-y^2 aligned 4 pq =2 x ^2-2 y ^2 ...(1) Now, p^2+q^2=x^2 ^2 +y^2 ^2 -2 x y +x^2 ^2 +y^2 ^2 +2 x y =x^2+y^2 ...(2) From (1), (2), aligned p^2+q^2+4 p q & =x^2+y^2+2 x^2-2 y^2 & =3 x^2-y^2 aligned Comparing this with the given form, we get = 4 , A=3, B=-1