If x = 2√5 + √3 and y = 2√5 - √3, evaluate x2 + y2
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For this question answer is 4√5
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x = 2√5 + √3
y = 2√5 - √3
x² + y² = (2√5 + √3)² + (2√5 - √3)²
= (2√5)²+2(√3)(2√5)+(√3)² + (2√5)²+2(√3)(2√5)-(√3)²
= 20+ 4√15 +3 + 20+ 4√15 -3
= 40 + 8√15
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