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Question 136
If $$p(x+y)^{2}=5$$ and $$q(x-y)^{2}=3$$, then the simplified value of $$p^{2}(x+y)^{2}+4\ pq\ xy - q^{2}(x-y)^{2}$$ is:
Solution
We have :
(x+y)^2 =5/p Â
we get x^2+y^2+2xy =5/p (1)
NowÂ
(x-y)^2=3/q
x^2+y^2-2xy =3/q          (2)
Subtracting (1) and (2)
4xy = 5/p -3/q
we get 4pqxy =5q-3p   (3)
Now p^2(x+y)^2+4pqxy -q^2(x-y)^2
we get p^2(5/p)-q^2(3/q)+5q-3p
we get 2p+2q
= 2(p+q)
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