Question

已知：x=√3-√2/√3+√2 , y=√3+√2/√3-√2 , 那么代数式3x^2-5xy+3y^2的值为？

Answer 1

x=(√3-√2)/(√3+√2)
=(√3-√2)*(√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=(√3-√2)/(√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(-4√6)^2+1
=289

Answer 2

x=(√3-√2)^2/(√3+√2) (√3-√2)
=5-2√6,
y=√3+√2/√3-√2=5+2√6
x^2+y^2=25+24-20√6+25+24+20√6=98
xy=25-24=1
3x^2-5xy+3y^2=3(x^2+y^2)-5x=3*98-5=289