若方程2x²-2x-1=0的两个根为x1,x2,不解方程,求下列各式的值①x1²+x2² ②x1²-x2² ③x2/x1+x1/x2 ④2x2²-x1x2+2x1-3
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![若方程2x²-2x-1=0的两个根为x1,x2,不解方程,求下列各式的值①x1²+x2² ②x1²-x2² ③x2/x1+x1/x2 ④2x2²-x1x2+2x1-3](/uploads/image/z/3762926-62-6.jpg?t=%E8%8B%A5%E6%96%B9%E7%A8%8B2x%26%23178%3B-2x-1%3D0%E7%9A%84%E4%B8%A4%E4%B8%AA%E6%A0%B9%E4%B8%BAx1%2Cx2%2C%E4%B8%8D%E8%A7%A3%E6%96%B9%E7%A8%8B%2C%E6%B1%82%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F%E7%9A%84%E5%80%BC%E2%91%A0x1%26%23178%3B%2Bx2%26%23178%3B+%E2%91%A1x1%26%23178%3B-x2%26%23178%3B+%E2%91%A2x2%2Fx1%2Bx1%2Fx2+%E2%91%A32x2%26%23178%3B-x1x2%2B2x1-3)
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若方程2x²-2x-1=0的两个根为x1,x2,不解方程,求下列各式的值①x1²+x2² ②x1²-x2² ③x2/x1+x1/x2 ④2x2²-x1x2+2x1-3
若方程2x²-2x-1=0的两个根为x1,x2,不解方程,求下列各式的值
①x1²+x2² ②x1²-x2² ③x2/x1+x1/x2 ④2x2²-x1x2+2x1-3
若方程2x²-2x-1=0的两个根为x1,x2,不解方程,求下列各式的值①x1²+x2² ②x1²-x2² ③x2/x1+x1/x2 ④2x2²-x1x2+2x1-3
(根号下不会打..用√ 代替,抱歉.)
x1+x2=﹣b/a=1 x1x2=c/a=﹣1/2
①:x1²+x2²=(x1+x2)²-2x1x2=1+1=2
②:x1-x2=√(x1-x2)²=√[﹙x1+x2﹚²-4x1x2)]=√3
x1²-x2²=(x1+x2)(x1-x2)=√3
③x2/x1+x1/x2=x2²+x1²/x1x2=-4
④∵x2为方程的根,把x2带入∴2x2²-2x2-1=0 即2x2²=1+2x2
2x2²-x1x2+2x1-3=1+2x2-x1x2+2x1-3=2(x1+x2)-x1x2-2=1/2