作业帮x=(根号3-根号2)/(根号3+根号2),y=(根号3+根号2)(根号3-根号2),求代数式3x^2-5xy+3y^2的值
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x=(根号3-根号2)/(根号3+根号2),y=(根号3+根号2)(根号3-根号2),求代数式3x^2-5xy+3y^2的值
x=(√2-√3)/(√3+√2)
=(√2-√3)*(√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=(√2-√3)/(√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(-10)^2-1
=300-1
=299
x=(根号3-根号2)/(根号3+根号2)=(√3-√2)(√3-√2)/(√3+√2)(√3-√2)=(√3-√2)²
y=(根号3+根号2)(根号3-根号2),=(√3+√2)(√3+√2)/(√3-√2)(√3+√2)=(√3+√2)²
∴3x²-5xy+3y²
=3x²-6xy+3y²+xy
=3(...
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x=(根号3-根号2)/(根号3+根号2)=(√3-√2)(√3-√2)/(√3+√2)(√3-√2)=(√3-√2)²
y=(根号3+根号2)(根号3-根号2),=(√3+√2)(√3+√2)/(√3-√2)(√3+√2)=(√3+√2)²
∴3x²-5xy+3y²
=3x²-6xy+3y²+xy
=3(x-y)²+xy
=3[(√3-√2)²-(√3+√2)²]+(√3-√2)(√3+√2)
=3(√3-√2+√3+√2)(√3-√2-√3-√2)+(3-2)
=3×2√3×(-2√2)+1
=-12√6+1
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x=(√3-√2)/(√3+√2)，y=(√3+√2)/(√3-√2),
y-x=((√3+√2)*(√3+√2)-(√3-√2)*(√3-√2))/(3-2)=4√6
x=1/y;
xy=1;
3x²-6xy+3y²+xy
=3(x-y)²+xy
=3*4*4*6+1=16*18+1=17*17=288呃，好像是对的，...
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x=(√3-√2)/(√3+√2)，y=(√3+√2)/(√3-√2),
y-x=((√3+√2)*(√3+√2)-(√3-√2)*(√3-√2))/(3-2)=4√6
x=1/y;
xy=1;
3x²-6xy+3y²+xy
=3(x-y)²+xy
=3*4*4*6+1=16*18+1=17*17=288
收起