Question

Rezolvati ecuatia I 5x+6 I≥ 3

Answer 1

(5x+6)²≥3²
(5x)²+2*5x*6+6²≥9
25x²+60x+36≥9
25x²+60x+27≥0
f(x)=25x²+60x+27
f(x)=0
25x²+60x+27=0
Δ=b²-4ac=60²-4*25*27=3600-2700=900
x₁=$\frac{-b+ \sqrt{d} }{2a} = \frac{-60+ \sqrt{900} }{2*25} = \frac{-60+30}{50}= \frac{-30}{50} = -\frac{3}{5}$
x₂=$\frac{-b- \sqrt{d} }{2a} = \frac{-60- \sqrt{900} }{2*25} = \frac{-60-30}{50} = \frac{-90}{50} =- \frac{9}{5}$

faci axa
si S=(-∞;-9/5]∪[-3/5;+∞)