Question

a、b是实数,如果已知4/a4-4/a2-3=0,且b4+2b2-3=0,那么a4xb4+4/a4=

Answer 1

设：α=1/a^2,必有α>0

则,4α^2-4α-3=0

(2α-3)(2α+1)=0

α=3/2,α=-1/2(因为α>0,舍去）

设：β=b^2,同样β必然大于0.

β^2+2β-3=0

(β-1)(β+3)=0

β=1,β=-3(因为β>0,舍去)

a4xb4+4/a4

=(1/α)^2*β^2+4*α^2

=(2/3)^2*1+4*(3/2)^2

=4/9+9

=85/9