Question 981899
The equation 8x-x^2=k-2 has roots a and b. Find the value of k if the roots differ by 2.

x^2-8x+(k-2) =0

a+b = -(-8)/1 =8

ab = k-2

a-b =2

a+b= 8
a-b= 2

2a=10
a=5

a-b =2
b=3

ab = k-2

5*3 = k-2

15 =k-2
k=17