Question

Who can solve the following math problems?

Answer 1

1.2.3

(b)

let D(n) be the final answer

we have

D(n)=aD(n-1)-D(n-2)

D(1)=a

D(2)=a^2-1

(c)

let D(n) be the final answer

we have

D(n)=aD(n-1)+(b^2)[(a+b)^(n-2)]

D(1)=a

1.3.4

if a+b+c=0

then,(x,y)=(1,1) satisfied all three equations,which means these three line pass the point(1,1).

if these lines pass one point

then,

ax+by+c=0

bx+cy+a=0

since lines are distinguished each other,

ac-b^2 != 0

x=(-c^2+ab)/(ac-b^2)

y=(-a^2+bc)/(ac-b^2)

from the last equation

c(-c^2+ab)/(ac-b^2)+a(-a^2+bc)/(ac-b^2)+b=0

we get

a^3+b^3+c^3-3abc=0

that is

(a+b+c)(a^2+b^2+c^2-ab-bc-ac)=0

(a+b+c)0.5((a-b)^2+(b-c)^2+(c-a)^2)=0

since a=b=c can not be reached,otherwise three lines are actually one line,0.5((a-b)^2+(b-c)^2+(c-a)^2)>0

so a+b+c=0