How do you solve the equation #absx=12-x^2#?

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Answer 1 · 2017-04-17T13:23:16

The Soln. Set =#{+-3}.#

Recall that, #|x|=x, if x ge 0; and, |x|=-x, if x lt 0.#

We can see from the eqn. that #x=0# does not satisfy the given eqn.

Therefore, we will consider only #2# Cases :

Case 1 : #x gt 0.#

In this case, taking, #|x|=x,# the eqn. becomes,

#x=12-x^2, or, x^2+x-12=0.#

#:. ul(x^2+4x)-ul(3x-12)=0,....[4xx3=12, 4-3=1]#

#:. x(x+4)-3(x+4)=0.#

#:. (x+4)(x-3)=0#

#:. x=-4, or, x=3.# Since, #x gt 0, x=3.#

Case 2 : #x<0.#

Here, since, #|x|=-x," we hvae, "x^2-x-12=0.#

#:. x=4, or, x=-3;" but, "x < 0 rArr x=-3.#

These roots satisfy the given eqn.

Hence, The Soln. Set =#{+-3}.#

Enjoy Maths.!