Plz EXPLAIN
Q.11. The sum of all the real roots of the equation x - 2 2 + x - 2 - 2 = 0 is?

Dear Student,

We have,x-22+x-2-2=0Let,x-22=ytherefore,y2+y-2=0y2+2y-y-2=0yy+2-1y+2=0y-1y+2=0y-1=0 y=1x-2=1x-2=±1x-2=1x=3 and x-2=-1x=1and,y+2=0y=-2but, x-2-2So, all the real roots are 1 and 3And the sum is 1+3= 4

Regards.

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|x-2|^{2} + |x-2| - 2 = 0

Let x to be greater than equal to 2.

(x-2)^{2} + (x-2) - 2 = 0x^{2} + 4 -4x + x-2 - 2 = 0x^{2} -3x = 0x = 0; 3

So x = 3 is only possible.
Let x to be less than 2.

|x-2|^{2} + |x-2| - 2 = 0x2– 5x + 4 = 0
x = 1, 4
x = 1 is only possible.

So, there are two roots 1 & 3.
Sum of roots is 4.

Hope it will help :)
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