x=√5-√3/√5+√3, y=√5+√3/√5-√3 find x^2 + y^2
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KeyaChincholkar:
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x = √5 - √3 = (√5 - √3) (√5 - √3) = (√5 - √3)² = 5 + 3 - 2√15
√5 + √3 (√5 + √3) (√5 - √3) (√5)² - (√3)² 5 - 3
= 8 - 2√15 = 4 - √15
2
x² = (4 - √15)² = 16 + 15 - 8√15 = 31 - 8√15
y = √5 + √3 = (√5 + √3) (√5 + √3) = (√5 + √3)² = 5 + 3 + 2√15
√5 - √3 (√5 - √3) (√5 + √3) (√5)² - (√3)² 5 - 3
= 8 + 2√15 = 4 + √15
2
x² = (4 + √15)² = 16 + 15 + 8√15 = 31 + 8√15
x² + y² = 31 - 8√15 + 31 + 8√15 = 62
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