Given $(x^{2}+y^{2})$=74 and xy =35, find the value of:a) x+yb) x-y

Given $(x^{2} + y^{2})$ = 74; xy = 35

To find: 

a) $x+y$

b)$x-y$

Solution:

a)

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

= $74 + 2(35)$

= $74 + 70 = 144$

So $x + y$ = 12 or -12

b)

$(x - y ) ^ {2} = x^{2} + y^{2} - 2xy$

= $74 - 2(35) = 74 - 70 = 44$

$x - y$ = 2 or -2

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Updated on: 10-Oct-2022

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