Question

Rezolvati ecuatia: ||x-5|-2|=3

Answer 1

||x-5|-2|=3

|x-5|-2=+-3

|x-5|-2=-3. ............. sau.........…..|x-5|-2=3

|x-5|=-3+2.....................................|x-5|=3+2

|x-5|= - 1...........................................|x-5|=5

x1= mulțimea vidă

|x-5|=5

x-5=+-5

x-5=-5 ..............sau.........x-5=5

x2=-5+5...............sau .......x3=5+5

x2=0 ....................sau .......x3=10

x={0;10}

S={0;10}

Answer 2

||x-5|-2|=3

||x-5|-2|= -3

||x-5|-2|=3

|x-5|= 3+2

x-5=5 => x = 10

x-5= -5 => 0

||x-5|-2|= -3

|x-5|= -3+2

|x-5|=-1 = nu se poate =>

x ∈ ∅

☕︎︎ Ecuația are 2 soluții:

x¹=0

x²=10

S={0;10}

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