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the sum of all real root of the equation ​/x-2/ 2 + /x-2/ – 2=0

the sum of all real root of the equation
​/x-2/2 + /x-2/ – 2=0

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find the answer to your question below
|x-2|^{2} + |x-2| - 2 = 0
Let x to be greater than equal to 2.
(x-2)^{2} + (x-2) - 2 = 0
x^{2} + 4 -4x + x-2 - 2 = 0
x^{2} -3x = 0
x = 0; 3
So x = 3 is only possible.
Let x to be less than 2.
|x-2|^{2} + |x-2| - 2 = 0
x2– 5x + 4 = 0
x = 1, 4
x = 1 is only possible.
So, there are two roots 1 & 3.
Sum of roots is 4.

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