Question 990548
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<B>Answer</B>. &nbsp;a) &nbsp;4 &nbsp;and &nbsp;2; &nbsp;&nbsp;b) &nbsp;-2 &nbsp;and &nbsp;-4.


<B>Solution</B>


x - y = 2; &nbsp;&nbsp;----->


{{{(x-y)^2}}} = {{{4}}}, &nbsp;&nbsp;----->


{{{x^2 - 2xy + y^2}}} = 4, &nbsp;&nbsp;(recall that &nbsp;&nbsp;{{{x^2 + y^2 = 20}}}) ----->


{{{20 - 2xy}}} = {{{4}}}, ----->


2xy = 20 - 4 = 16, ----->


xy = {{{16/2}}} = 8. ----->


{{{system(x-y=2,
xy = 8)}}}. ----->


x = 2+y ----->


(2+y)*y = 8, ----->


{{{y^2 + 2y - 8}}} = {{{0}}} ----->


The roots are &nbsp;&nbsp;{{{y[1]}}} = 2, &nbsp;&nbsp;{{{y[2]}}} = -4 &nbsp;&nbsp;(use the quadratic formula or the Viete's theorem). ----->


The solutions are &nbsp;&nbsp;(x,y) = (4.2) &nbsp;&nbsp;and &nbsp;&nbsp;(x,y) = (-2, -4).