Question

$| (x+1)^{2}-x(x-5)|=6$

Answer 1

I(x + 1)² - x(x - 5) I = 6
Desfacem parantezele:

I x² + 2x + 1 - x² + 5x I = 6
x² se reduce cu -x²

I 2x + 1 + 5x I = 6

I 7x + 1 I = 6

Dexcompunem ecuatia in doua ecuatii

Daca (7x + 1)  ≥ 1   ⇒   7x + 1 = 6  ⇒ 7x = 5   ⇒  x₁ = 5 / 7

Daca (7x + 1) < 0  ⇒ -(7x + 1) = 6  ⇒ -7x - 1  = 6  ⇒ -7x  = 7  ⇒ x = - 7 / 7 = -1

Answer 2

|x^2+2x+1-x^2+5x|=6
|7x+1|=6
I daca 7x+1>0 adica 7x> -1 ⇒ x > -1/7 avem 7x+1=6⇒ 7x=5 ⇒ x=5/7 este solutia
II daca 7x+1< sau egal cu 0 ⇒ x< -1/7 avem -7x-1=6 ⇒ - 7 x = 7 ⇒ x= -1 care nu apartine (- infinit, - 1 /7) deci singura solutie este 
x=5/7