已知方程x²+3X-1=0的两实数根为X1,X2,不解方程求下列各式的值
问题描述:
已知方程x²+3X-1=0的两实数根为X1,X2,不解方程求下列各式的值
(1)1/x1+1/x2
(2)x1²﹢x2²
(3)﹙x1﹣1﹚﹙x2﹣1﹚
答
x1+x2 = -3,x1x2 = -1
1/x1 + 1/x2 = (x1+x2)/x1x2 =3
x1^2 + x2^2 =(x1+x2)^2 - 2x1x2 = 9+2 = 11
(x1-1)(x2-1) = x1x2 +1 - (x1+x2) = -1 +1 +3 = 3