已知x=√3+√2,y=√3-√2,求代数式3x²-5xy+3y²的值

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3x²-5xy+3y²
=3x²-6xy+3y²+xy
=3(x²-2xy+y²)+xy
=3(x-y)²+xy
=3[√3+√2-(√3-√2)]^2+(√3+√2)(√3-√2)
=3[√3+√2-√3+√2]^2+1
=3(2√2)^2+1
=3*8+1
=24+1
=25

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