Q2 Consider the following three conditions (a), (b) and (c) on two real numbers $x$ and $y$: (a) $x+y=5$ and $xy=3$, (b) $x+y=5$ and $x^2+y^2=19$, (c) $x^2+y^2=19$ and $xy=3$. (1) Using the equality $x^2+y^2=(x+y)^2 - \square\mathbf{F}\, xy$, we see that $$\text{condition (b) gives } xy = \mathbf{G},$$ $$\text{condition (c) gives } x+y = \mathbf{H} \text{ or } x+y = \mathbf{IJ}.$$ (2) For each of the following $\mathbf{K} \sim \mathbf{M}$, choose the most appropriate answer from among the choices (0)$\sim$(3) below. (i) (a) is $\mathbf{K}$ for (b). (ii) (b) is $\mathbf{L}$ for (c). (iii) (c) is $\mathbf{M}$ for (a). (0) a necessary and sufficient condition (1) a sufficient condition but not a necessary condition (2) a necessary condition but not a sufficient condition (3) neither a necessary condition nor a sufficient condition
Q2 Consider the following three conditions (a), (b) and (c) on two real numbers $x$ and $y$:
(a) $x+y=5$ and $xy=3$,
(b) $x+y=5$ and $x^2+y^2=19$,
(c) $x^2+y^2=19$ and $xy=3$.
(1) Using the equality $x^2+y^2=(x+y)^2 - \square\mathbf{F}\, xy$, we see that
$$\text{condition (b) gives } xy = \mathbf{G},$$
$$\text{condition (c) gives } x+y = \mathbf{H} \text{ or } x+y = \mathbf{IJ}.$$
(2) For each of the following $\mathbf{K} \sim \mathbf{M}$, choose the most appropriate answer from among the choices (0)$\sim$(3) below.
(i) (a) is $\mathbf{K}$ for (b).
(ii) (b) is $\mathbf{L}$ for (c).
(iii) (c) is $\mathbf{M}$ for (a).
(0) a necessary and sufficient condition
(1) a sufficient condition but not a necessary condition
(2) a necessary condition but not a sufficient condition
(3) neither a necessary condition nor a sufficient condition