Question

若X²-X-2=0,则（X²-X）²-1+根号3分之X²-X+2根号3的值等于

Answer 1

∵X²-X-2=0

∴x²-x=2

（X²-X）²-1+根号3分之X²-X+2根号3

=[(x²-x+2√3]/[(x²-x)²-1+√3]

=(2+2√3)/(4-1+√3)

=(2+2√3)(3-√3)/(3+√3)(3-√3)

=(6+6√3-2√3-6)/(9-3)

=4√3/6

=2√3/3