Question

已知:a的平方减4a+1等于0 求：a的平方+a的平方分之1的值

Answer 1

∵a²-4a-1=0, 有 a²=4a+1

∴(a-1/a)²=a²+1/a²-2

=(4a+1)+1/(4a+1)-2

=[(4a+1)²+1-2(4a+1)]/(4a+1)

=(16a²+1+8a+1-8a-2)/(4a+1)

=16(4a+1)/(4a+1)

=16

即 a-1/a=4或a-1/a=-4