Question

x=(根号3-根号2)/(根号3+根号2)，y=(根号3+根号2)(根号3-根号2),求代数式3x^2-5xy+3y^2的值

要快！

Answer 1

x=(√2-√3)/(√3+√2)
=(√2-√3)*(√3-√2)/((√3+√2)*(√3-√2))
=(-5+2√6)/(3-2)
=-5+2√6
y=(√3+√2)/(√3-√2)
=(√3+√2)*(√3+√2)/(√3-√2)*(√3+√2))
=(5+2√6)/(3-2)
=5+2√6
x*y=(√2-√3)/(√3+√2)*(√3+√2)/(√3-√2)
= -1
3x^2-5x*y+3y^2 =3(x^2-2x*y+y^2)+x*y
=3(x-y)^2+x*y
=3(-5+2√6-(5+2√6))^2+(-1)
=3(-5+2√6-5-2√6)^2+(-1)
=3(-10)^2-1
=300-1
=299

追问

9到10排x*y为什么等余-1？你这片是抄的，我正在看，但还是请你解释下，谢谢！

追答

x*y=(√2-√3)/(√3+√2)*(√3+√2)/(√3-√2)
=1

追问

那是写错了吗？还是全部错了？

追答

√2-√3与√3-√2看错了
全部错了

追问

哦，但 x*y=(√2-√3)/(√3+√2)*(√3+√2)/(√3-√2)
= -1
3x^2-5x*y+3y^2 =3(x^2-2x*y+y^2)+x*y
=3(x-y)^2+x*y
=3(-5+2√6-(5+2√6))^2+(-1)
=3(-5+2√6-5-2√6)^2+(-1)
=3(-10)^2-1
=300-1
=299 上面的都是对的吗？

追答

没法改了

追问

知道了，全部错了

追答

x=5-2√6
y=5+2√6
x*y=1
3x^2-5x*y+3y^2 =3(x^2-2x*y+y^2)+x*y
=3(x-y)^2+x*y
=3(5-2√6-(5+2√6))^2+1
=3(-4√6)^2+1=3*16*6+1=289

Answer 2

x=(根号3-根号2)/(根号3+根号2)=(√3-√2)(√3-√2)/(√3+√2)(√3-√2)=(√3-√2)²
y=(根号3+根号2)(根号3-根号2),=(√3+√2)(√3+√2)/(√3-√2)(√3+√2)=(√3+√2)²
∴3x²-5xy+3y²
=3x²-6xy+3y²+xy
=3(x-y)²+xy
=3[(√3-√2)²-(√3+√2)²]+(√3-√2)(√3+√2)
=3(√3-√2+√3+√2)(√3-√2-√3-√2)+(3-2)
=3×2√3×(-2√2)+1
=-12√6+1

Answer 3

x=(√3-√2)/(√3+√2)，y=(√3+√2)/(√3-√2),
y-x=((√3+√2)*(√3+√2)-(√3-√2)*(√3-√2))/(3-2)=4√6
x=1/y;
xy=1;
3x²-6xy+3y²+xy
=3(x-y)²+xy
=3*4*4*6+1=16*18+1=17*17=288

追问

呃，好像是对的，顺便帮我指下我上面的追问是什么回事？谢谢

追答

3x²-6xy+3y²+xy
=3(x-y)²+xy
=3*4*4*6+1=16*18+1=17*17=289