Question

Решите неравенство (х+5)^2<=25-х^2​

Answer 1

Ответ:

(х+5)^2<=25-х^2

(x+5)^2<=(5-x)(5+x)

(5+x)×(x+5-(5-x))<=0

(5+x)×(x+5-5+x)<=0

(5+x)×(x+x)<=0

(5+x)×2x<=0

{5+x <=0

{2x>=0

x<= -5

x >= 0

x€[-5;0]

Answer 2

(x + 5)² ≤ 25 - x²

x² + 10x + 25 - 25 + x² ≤ 0

2x² + 10x ≤ 0

x² + 5x ≤ 0

x(x + 5) ≤ 0

    +               -             +

_____[- 5]_____[0]_____

            ////////////////

Ответ : x ∈ [- 5 , 0]