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Question

Solve the following systems of equations.
x2+y2=41,x+y=9

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Solution

Given that x2+y2=41 and x+y=9
now we have,
(x+y)2=x2+y2=2xy
Now put the given value
(9)2=41+2xy
2xy=8141=40
xy=20
(xy)2=(x+y)24xy
(xy)2=(9)24×20
(xy)2=8180=1
(xy)2=1
So, (xy)=1,1

(x+y)=9...........(a)

(xy)=1........(b)
Now add (a) and (b), we have
2x=10
x=5
and y=95=4
For (xy)=1
x=4 and y=94=5

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