已知x=√3+√2÷√3-√2,y=√3-√2÷√3+√2,则代数式3x²-5xy+3y²的值为
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![已知x=√3+√2÷√3-√2,y=√3-√2÷√3+√2,则代数式3x²-5xy+3y²的值为](/uploads/image/z/1108698-42-8.jpg?t=%E5%B7%B2%E7%9F%A5x%3D%E2%88%9A3%2B%E2%88%9A2%C3%B7%E2%88%9A3-%E2%88%9A2%2Cy%3D%E2%88%9A3-%E2%88%9A2%C3%B7%E2%88%9A3%2B%E2%88%9A2%2C%E5%88%99%E4%BB%A3%E6%95%B0%E5%BC%8F3x%26%23178%3B-5xy%2B3y%26%23178%3B%E7%9A%84%E5%80%BC%E4%B8%BA)
已知x=√3+√2÷√3-√2,y=√3-√2÷√3+√2,则代数式3x²-5xy+3y²的值为
已知x=√3+√2÷√3-√2,y=√3-√2÷√3+√2,则代数式3x²-5xy+3y²的值为
已知x=√3+√2÷√3-√2,y=√3-√2÷√3+√2,则代数式3x²-5xy+3y²的值为
x=﹙√3+√2﹚/﹙√3-√2﹚=5+2√6
y=﹙√3-√2﹚/﹙√3-√2﹚=5-2√6
x·y=﹙5+2√6﹚﹙5-2√6﹚=1
x-y=5+2√6-5+2√6=4√6
∴ 3x²-5xy+3y²
=3﹙x-y﹚²+xy
=3×﹙4√6﹚²+1
=3×96+1
=289
x=√3+√2÷√3-√2,y=√3-√2÷√3+√2
x=5+2√6
y=5-2√6
xy=25-24=1
x+y=10
所以
3x²-5xy+3y²
=3(x²+2xy+y²)-11xy
=3(x+y)²-11xy
=3×100-11
=300-11
=289
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