Question
If x = (2+√3)/(2-√3), y = (2-√3)/(2+√3)
Then find out the value of (x²+y²-xy)/(x²+y²+xy)Solution
x = (2+√3)/(2-√3) y = (2-√3)/(2+√3) So x+y = (2+√3)/(2-√3) + (2-√3)/(2+√3) = ((2+√3)²+ (2-√3)²)/((2)²- (√3)²) = 2(4+3)/(4-3) = x+y = 14 = xy = 1 (a+b)² + (a-b)² = 2(a^2+b^2 ) (a+b) + (a-b) = (a^2-b^2 ) = (x2+y2-xy)/(x2+y2+xy) = ((x+y)²-3xy)/((x+y)²-xy) = ((14)2-3 ×1)/((14)2-1) = (196-3)/(196-1) = 193/195
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