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please tell me the besic concept utilized to calculate total number of real solutions of a given function for eg.The number of real solutions of, 1 + | ex – 1| = ex(ex- 2]

please tell me the besic concept utilized to calculate total number of real solutions of a given function for eg.The number of real solutions of,
1 + | ex – 1| = ex(ex- 2]

Grade:12

1 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
7 years ago
1. the the way to find number of solution is sketching the curve of such function, and find out the number of intersection point.
2. by heat and trial, put some values of x , and try to see that if function satisfy or not.
3. put e^x=y
1+|y-1|=y(y-2)
for y>1
1+y-1=y^2-2y
y^2-3y=0, y=0 or y=3 , then put back e^x=3
for y<1
1+-y+1=y^2-2y
y^2-2y-2=0
solve above equation

sher mohammad
b.tech, iit delhi

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