SOLUTION: if x + y =12 and xy = 163, find x squared + y squared
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Question 177583: if x + y =12 and xy = 163, find x squared + y squared
Found 2 solutions by edjones, solver91311:
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
x+y=12
xy=163
.
x=12-y
y(12-y)=163
12y-y^2=163
y^2-12y+163=0
y=6-sqrt(127)i, x=6+sqrt(127)i (or vice versa) [quadratic equation]
x^2+y^2
=[-91+12sqrt(127)i]+[-91-12sqrt(127)i]
=182
.
Ed
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Hence:
y = 12y-y^2 = 163)
Put in standard form and solve:
 \pm {sqrt{(-12)^2-4(1)(-163)}}} {2*1}=6 \pm i sqrt{127})
Therefore:  = 6 \mp i sqrt{127})
So:
and
Either way,
^2 + (6 - i sqrt{127})^2)
^2 + (6 - i sqrt{127})^2= (36 + 12 i sqrt(127) - 127) + (36 - 12 i sqrt{127} - 127) = 2( 36 - 127 ) = 2 * -91 = -182)
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