幾題數學題....幫個忙= =

Question

1.(m,n)=( , )使得d=m*725+n*2987 求m.n

2.I x+y-8 I+(x-2+1)^2=0,則3x-4y+5=? (I x+y-8 I為絕對值)

3.a.b為實數.已知2i為x^2+ax+1+bi=0的一根.則數對(a.b)=?
求a=?.b=?

Answer 1

Q1.
(725,2987)=29
29=725-87*8
=725-(2987-725*4)*8
=33*725-8*2987
故m=33,n=-8
Q2.
因為I x+y-8 I+(x-2+1)^2=0
x-2+1=0 =>x=1
又x+y-8=0 =>y=7
則3x-4y+5=3-28+5= -20

Answer 2

3.若非題目出錯就是無解,因為x=2i帶入得 -4+2ai+1+bi=-3+(2a+b)i=0,
但a,b為實數,故(2a+b)i為虛數,-3+(2a+b)i不可能為0.