初三数学题,求速解,200分要详细过程1.已知方程X²-3X+1=0,求代数式X²+1/X²的值.2.已知a=-2014,b=2011,c=-2009,求2a²+2b²+2c²+2ab+2bc-2ac的值.
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![初三数学题,求速解,200分要详细过程1.已知方程X²-3X+1=0,求代数式X²+1/X²的值.2.已知a=-2014,b=2011,c=-2009,求2a²+2b²+2c²+2ab+2bc-2ac的值.](/uploads/image/z/4106280-48-0.jpg?t=%E5%88%9D%E4%B8%89%E6%95%B0%E5%AD%A6%E9%A2%98%2C%E6%B1%82%E9%80%9F%E8%A7%A3%2C200%E5%88%86%E8%A6%81%E8%AF%A6%E7%BB%86%E8%BF%87%E7%A8%8B1.%E5%B7%B2%E7%9F%A5%E6%96%B9%E7%A8%8BX%26%23178%3B-3X%2B1%3D0%2C%E6%B1%82%E4%BB%A3%E6%95%B0%E5%BC%8FX%26%23178%3B%2B1%2FX%26%23178%3B%E7%9A%84%E5%80%BC.2.%E5%B7%B2%E7%9F%A5a%3D-2014%2Cb%3D2011%2Cc%3D-2009%2C%E6%B1%822a%26%23178%3B%2B2b%26%23178%3B%2B2c%26%23178%3B%2B2ab%2B2bc-2ac%E7%9A%84%E5%80%BC.)
初三数学题,求速解,200分要详细过程1.已知方程X²-3X+1=0,求代数式X²+1/X²的值.2.已知a=-2014,b=2011,c=-2009,求2a²+2b²+2c²+2ab+2bc-2ac的值.
初三数学题,求速解,200分
要详细过程
1.已知方程X²-3X+1=0,求代数式X²+1/X²的值.
2.已知a=-2014,b=2011,c=-2009,求2a²+2b²+2c²+2ab+2bc-2ac的值.
初三数学题,求速解,200分要详细过程1.已知方程X²-3X+1=0,求代数式X²+1/X²的值.2.已知a=-2014,b=2011,c=-2009,求2a²+2b²+2c²+2ab+2bc-2ac的值.
1.由X²-3X+1=0得x≠0,两边同除以x,得x+1/x=3,∴x^2+2+1/x^2=9
∴X²+1/X²=7
2.2a²+2b²+2c²+2ab+2bc-2ac=(a+b)^2+(b+c)^2+(a-c)^2=9+4+25=38
1.∵X²-3X+1=0,X≠0,∴方程两边同÷X得:x-3+1/X=0,X+1/X=3 X²+1/X²=(X+1/X)²-2=9-2=7 2.2a²+2b²+2c²+2ab+2bc-2ac=(a²+2ab+b²)+(b²+c²+2bc)+(a²+c²-2ac)=(a+b)²+(b+c)²+(a-c)²=9+4+25=38
1.
X²-3X+1=0;X²+1=3X;X+1/X=3;
X²+1/X²=(X+1/X)*2-2=9-2=7
2.
2a²+2b²+2c²+2ab+2bc-2ac=(a+b)*2+(b+c)*2+(a-c)*2=9+9+25=43
x2+1=3x 左右除以X 得到x+1/x=3 然后平方 x2+1/x2=7
第二式 原式=(a+b)2+(b+c)2+(a-c)2 然后带入
1. 7