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Comment on Absolute Solution Sum
why not (d) 12 is the correct
I can't really help you
I can't really help you unless you tell me how you arrived at 12.
sir why cant we solve the
for example.
|x-3|^2+|x-3|=20
=> x^2 + 9 -6x + x - 3 = 20
=> x^2 - 5x - 14 = 0
=>(x-7)(x+2)= 0
so either x = +7 or x = -2
but substituting x=7 and x=-2 in the eqn we find out that x=7 gives us 20=20 (satisfies eqn), where as x=-2 does not satisfy the eqn.
so therefore sum= 7
Your approach is to ignore
Your approach is to ignore the absolute value notation altogether. This causes you to miss one of the solutions (x = -1).
Consider this equation: |x + 1| = 3
If we just ignore the absolute value notation (as you did), then we get the equation x + 1 = 3
Solve to get x = 2
As you can see, by ignoring the absolute value notation, you miss the possibility that x + 1 = -3, in which case x = -4
So, as you can see, ignoring the absolute value notation will cause you to miss certain solutions.
got it :) Thanks !!!
Is there a reason you didn't
That's a great point. I
That's a great point. I should have checked for extraneous roots.
That said, we need not plug the values into the original equation, because we already learned that either |x-3| = -5 or |x-3| = 4.
Since we determined that |x-3| = -5 is unsolvable, we need only plug our two answer choices into the equation |x-3| = 4 to look for extraneous roots.
Hello,
I arrived at the answer option d, which is 12. Plz find the approach below and let me know where did I go wrong:
|x-3|^2 + |x - 3| = 20 (Given)
Since the absolute value can take two forms, there are two solving giving rise to 4 values for X.
Approach 1:
(x-3)^2 + (x-3) = 20
solving this, we get x = 7 and -2
Approach 2:
(3-x)^2 + (3-x) = 20
solving this, we get x = 8 and x = -1
(how I approached this method can be explained by another eg as I am finding it difficult to brief. Let |x-3|=2, then x can take value 5(x-3=2) and 1(3-x=2) and this satisfies the equation as well)
Sum of all solutions : 7-2+8-1 = 12
All solution satisfies the equation as well.
Two of your solutions don't
Two of your solutions don't satisfy the original equation.
We'll start with x = -2
Plug into equation to get: |-2 - 3|² + |-2 - 3| = 20
|-5|² + |-5| = 20
25 + 5 = 20
30 = 20
NO GOOD
Now test x = 8
Plug into equation to get: |8 - 3|² + |8 - 3| = 20
|5|² + |5| = 20
25 + 5 = 20
30 = 20
NO GOOD
I now get it.. Thank you!!!
Great unique problem! Thank
That's nice of you to say.
That's nice of you to say. Thanks!