Question

2m²-4= I 5m-9 I

barele alea 2 ar trebui sa reprezinte modulul

Aflati m ∈ R

Answer 1

Ai doua cazuri
1) 5m-9>0 ⇒ 5m>9 ⇒ m>9/5
2m² - 4= 5m-9 ⇒ 2m² - 5m +5=0 ⇒ Δ=25-40=-15<0 ⇒ ec. nu admite sol. reale
2)5m-9<0 ⇒ 5m<9 ⇒ m<9/5
2m² - 4= -5m + 9 ⇒ 2m² + 5m -13 =0 ⇒ Δ=25 + 4*2*13=25+104=129 ⇒ √Δ= +/- √129
m1=$\frac{-5+ \sqrt{129} }{4}$ <9/5
m2=$\frac{-5- \sqrt{129} }{4}$ <9/5
S={  $\frac{-5+ \sqrt{129} }{4}$ ,  $\frac{-5- \sqrt{129} }{4}$ }