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