Question

已知X1和X2是一元二次方程4倍K乘以X的平方减4倍KX加K加1等于0的两个实数根.

Answer 1

1.x1+x2=1 x1x2=(k+1)/4k(2x1-x2)(x1-2x2)=2x1^2-5x1x2+2x2^2=2(x1+x2)^2-9x1x2=2-9(k+1)/4k=-3/2 k=9/52.x1/x2+x2/x1-2

=(x1^2+x2^2-2x1x2)/(x1x2)

=[(x1+x2)^2-4x1x2]/(x1x2)

=[1-4*(k+1)/(4k)]/(k+1)/(4k)

=-4/(k+1)

要使x1/x2+x2/x1-2 的值为整数,只须k＋1能整除4．而k为整数,

∴k＋1只能取±1,±2,±4．又∵k＜0,∴k＋1＜1,∴k＋1只能取－1,－2,－4,∴k＝－2,－3,－5．

∴能使x1/x2+x2/x1-2的值为整数的实数k的整数值为－2,－3和－5．