Question

已知实数x,y满足y=(√(x²-4)+√(4-x²)+1)/(x-2),求2x-3y的值

Answer 1

y=(√(x²-4)+√(4-x²)+1)/(x-2)

等式有意义需根式和分母均有意义

∴x²-4≥0且4-x²≥0 ,且x-2≠0

∴x²=4且x≠2

∴x=-2

y=1/(-2-2)=-1/4

∴2x-3y

=2×(-2)-3×(-1/4)

=-4+3/4

=-13/4