5lb. Ch. 9 pr. 38 / p. 386

[irs031]

If [x^2 - 6] = x, which of the following could be the value of X?
(brackets are absolute value)



I do not really understand why 3 is the correct answer.

This is a quadratic equation that has two solutions x= -3 and 2 when absolute value is positive and x=3 and -2 when absolute negative value is negative.

If you plug in 3
(3^2 - 6) = 9-6 = 3
-(3^2 - 6) = -9+6 = -3

if you plug in -2
((-2)^2 - 6) = 4 - 6 = -2
-((-2)^2 - 6) = -(4-6) = -(-2) = 2

Why D (3) is more correct answer than A (-2)?

[n00bpron00bpron00b]

If [x^2 - 6] = x, which of the following could be the value of X?
(brackets are absolute value)



I do not really understand why 3 is the correct answer.

This is a quadratic equation that has two solutions x= -3 and 2 when absolute value is positive and x=3 and -2 when absolute negative value is negative.

Set of values -

a) x = -3, 2
b) x = 3, -2

Re-substitute these values in the original equation.

a) when x = -3
|(-3)^2-6| = -3
|9-6|=-3
|3|=-3
3 = -3 (Invalid)

when x = +2
|(2)^2-6|=+2
|4-6|=+2
|-2|=+2
2=2 (valid). But +2 is not a part of answer choice

b) when x = 3, -2
|(3)^2-6| = 3
|9-6| = 3
|3|=3
3=3 (True)

when x = -2
|(-2)^2-6|=-2
|4-6|=-2
|-2|=-2
2=-2 (invalid)

hence ans. (d) = 3

[tommywallach]

Noob is right, but just in case you missed it, you seem to be forgetting that the right side of this equation can't be negative, because the left side is an absolute value (i.e. zero or positive). That's the issue.

-t