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

Ans:Hello Student,Please find the answer to your question belowLet x to be greater than equal to 2.So x = 3 is only possible.Let x to be less than 2.x2– 5x + 4 = 0x = 1, 4x = 1 is only possible.So, there are two roots 1 & 3.Sum of roots is 4.

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Grade 11Algebra

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

tanya

12 Years agoGrade 11

1 Answer

Jitender Singh

11 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.