Question

QUESTION----
If x+y = 7/2 and xy = 5/2; find:
1- x-y
2- x square - y square..
PLEASE HELP ME WITH THIS QUESTION......

Answer 1

hope it is helpful for you

Answer 2

Hey friend!!


Here's ur answer...


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$x + y = \frac{7}{2} \: \: \: \: \: \: xy = \frac{5}{2} \\ \\ squaring \: \\ (x + y {)}^{2} = { \frac{7}{2^{2} } }^{2} \\ \\ {x}^{2} + {y}^{2} + 2xy = \frac{49}{4} \\ \\ {x}^{2} + {y}^{2} + 2( \frac{5}{2} ) = \frac{49}{4} \\ \\ {x}^{2} + {y}^{2} = \frac{49}{4} - 5 \\ \\ {x}^{2} + {y}^{2} = \frac{49 - 20}{4} \\ \\ {x}^{2} + {y}^{2} = \frac{29}{4} \\ \\ now \: taking \: (x - y {)}^{2} \\ \\ = {x}^{2} + {y}^{2} - 2xy \\ = \frac{29}{4} - 5 \\ \\ = \frac{29 - 20}{4} \\ \\ = \frac{9}{4} \\ \\ (x - y {)}^{2} = \frac{9}{4} \\ \\ so \: \: \: x - y = \frac{3}{2} \: \: or \: \: - \frac{3}{2}$


Now,



$x - y = \frac{3}{2} - - - - (1) \\ \\ x + y = \frac{7}{2} - - - - (2) \\ \\ adding \: (1) \: and \: (2) \\ \\ x - y + x + y = \frac{3}{2} + \frac{7}{2} \\ \\ 2x = \frac{10}{2} \\ \\ x = \frac{5}{2 } \\ \\ put \: in \: (1) \\ \\ \frac{5}{2} - y = \frac{3}{2} \\ \\ - y = \frac{3}{2} - \frac{5}{2} \\ \\ y = \frac{2}{2} \\ \\ y = 1$



So,

${x}^{2} - {y}^{2} \\ \\ = ( \frac{5}{2} {)}^{2} - (1 {)}^{2} \\ \\ = \frac{25}{4} - 1 \\ \\ = \frac{25 - 4}{4} \\ \\ = \frac{21}{4} .$



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Hope it may help you....



Thank you :) :)))