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.!

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