Question

If x+y=$\frac{7}{2}$and xy=$\frac{5}{2}$;find:
(i) x-y
(ii) ${x}^{2} - {y}^{2}$

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Answer 1

• To find

(i) x-y

$\rightarrow \sf(x + y {)}^{2} = {(x)}^{2} + {(y)}^{2} - 2(xy) - - - (i)$

$\sf \rightarrow {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy$

$\sf \rightarrow \frac{49}{4} - \frac{5}{4} = {x}^{2} + {y}^{2}$

$\sf \rightarrow \frac{29}{4} = {x}^{2} + {y}^{2}$

Put (i)

$\sf \implies {(x - y)}^{2} = \frac{29}{4} - \frac{5}{4} = \frac{9}{4}$

$\therefore \sf \: x - y = + - \frac{3}{2}$

(ii) $\sf \bf{x}^{2} - {y}^{2}$

$\sf {x}^{2} - {y}^{2} = {(x - y)}^{2}$

$\sf \: x - y = \frac{3}{2} \: \\ \\ \sf\therefore \: {x}^{2} - {y}^{2} \implies \frac{ {3}^{2} }{ {2}^{2} } = \frac{ + - 9}{4}$

~Hope it helps you...