Question

|x+1||x+4|=1 find x. Please help me solve this. It is urgent

Answer 1

this is solved by breking mode.

case 1 :- x ≥ -1

then, (x +1)( x +4) = 1
x² + 5x + 4 = 1
x² + 5x + 3 = 0
use quadratic formula,

x = { -5±√(13)}/2

={ -5- √13}/2 , { -5+√13}/2

here x ≠ { -5-√13}/2 becoz x ≥ -1

hence, here x = {-5+√13}/2 is possible

case 2 :- when, -4 < x < -1

then, -(x+1)(x +4) = 1

-x² -5x -4 = 1

x² + 5x +5 = 0

x = { -5±√5}/2

x = { -5+√5}/2 , { -5-√5}/2 both are possible here becoz -4 < x < -1

case 3 :- when, x ≤ -4

then , { -(x +1)}{ -(x +4)} = 1

x² + 5x + 3 = 0

x = { -5-√13}/2 , { -5+√13}/2

but x ≠ { -5 + √13}/2 becoz , x ≤ -4


hnece, finally here we find the solutions of x are

x = { -5±√13}/2, { -5±√5}/2