Answer:
The value of a+b is 1.
Step-by-step explanation:
The given equation is
[tex]x^2-1x-90=0[/tex]
The middle term can be written as -10x+9x.
[tex]x^2-10x+9x-90=0[/tex]
[tex]x(x-10)+9(x-10)=0[/tex]
[tex](x-10)(x+9)=0[/tex]
Using zero product property, equate each factor equal to 0.
[tex]x-10=0\Rightarrow x=10[/tex]
[tex]x+9=0\Rightarrow x=-9[/tex]
The solutions of the given equation are {-9,10}.
[tex]\{a,b\}=\{-9,10\}[/tex]
[tex]a+b=-9+10=1[/tex]
Therefore the value of a+b is 1.
