Question

已知x=2+根号3，y=2-根号3，求下列各式的值（1）(Y/X)+(X/Y);(2)(X^2-XY+Y^2)/(X+Y)

Answer 1

x=2+根号3,
y=2-根号3
xy=1, x+y=4

（1）(Y/X)+(X/Y);
=(x^2+y^2)/xy
=[(x+y)^2-2xy]/xy
=(4^2-2*1)/1
=14

(2)(X^2-XY+Y^2)/(X+Y)
=[(x+y)^2-3xy]/(x+y)
=(4^2-3*1)/4
=13/4

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Answer 2

1、Y/X+X/Y=(Y²+X²)/XY=[(4-4根号3+3)+(4+4根号3+3)]/(4-3)=14

2、(X²-XY+Y²)/(X+Y)=[(X+Y)²-3XY]/(X+Y)=(16-3)/4=13/4

Answer 3

(1).(Y/X)+(X/Y)=(X²+Y²)/XY=((2+√3)²+(2-√3)²)/(2+√3)(2-√3)=(7+4√3+7-4√3)/(4-3)=14
(2).(x²-xy+y²)/(x+y)=((2+√3)²-(2+√3)(2-√3)+(2-√3)²)/(2+√3+2-√3)
=(4+4√3+3-4+3+4-4√3+3)/4=13/4=3.25

Answer 4

（1）先将分母通分即可，答案是24（2）第二个答案是：根号3-（1/4）