A) \( \Large x^{2}+ \left(3-x^{2}\right)=9 \) |
B) \( \Large \left(3+y\right)^{2}+y^{2}=9 \) |
C) \( \Large xy=0 \) |
D) \( \Large \left(x-y\right)^{2}=9 \) |
C) \( \Large xy=0 \) |
We have \( \Large x^{2}+y^{2}=9 \) ...(i)
and \( \Large x+y=3 \) ...(ii)
From equation (i) we get
\( \Large x^{2}+y^{2}=3^{2} \)
=> \( \Large x^{2}+y^{2}= \left(x+y\right)^{2} \) [using equation. (ii)]
=> \( \Large x^{2}+y^{2}=x^{2}+y^{2}+2xy \)
=> \( \Large 2xy = 0 \)
=> \( \Large xy = 0 \)