Question

已知x=√3-√2/√3+√2,y=√3+√2/√3-√2,求代数式3x²-5xy+3y²的值

Answer 1

x=(√3-√2)/(√3+√2)

x=(√3-√2)²/(√3+√2)(√3-√2)

x=5-2√6

y=(√3+√2)/(√3-√2)

y=(√3+√2)²/(√3+√2)(√3-√2)

y=5+2√6

3x²-5xy+3y²

=3x²-6xy+3y²+xy

=3(x²-2xy+y²)+xy

=3(x-y)²+xy

=3*[5-2√6-(5+2√6)]²+(5-2√6)(5-2√6)

=3*[5-2√6-5-2√6]²+(5-2√6)(5-2√6)

=3*[-4√6]²+1

=3*96+1

=289