Question

(x-2)^2+mod[x-2]-2=0 find sum of all real roots

Answer 1

Step-by-step explanation:

Let f(x)=∣x−2∣

For x>2,f(x)=x−2

for x<2,f(x)=2−x

Thus, for x>2 equation becomes (x−2)

2

+(x−2)−2=0

x

2

−3x=0

Thus, the root of equation x>2 is 3

For x<2 the equation becomes (x−2)

2

+(2−x)−2=0

x

2

−5x+4=0

(x−4)(x−1)=0

Root which is less than 2 is 1

Thus, roots of given equations are 3, 1

Sum will be 3+1=4