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Question

If x=3+23-2and y=3-23+2, find (x2 + y2).

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Solution

x =3+23-2×3+23+2=3+223-2=3+2+223=5+26Now,y =3-23+2×3-23-2=3-223-2=3+2-223=5-26Thus, we have:xy=5+265-26=25-24=1x+y=5+26+5-26x+y=10Squaring both sides, we get:x+y2=102x2+y2+2xy=100x2+y2+2×1=100x2+y2=100-2=98

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