Question

VA IMPLOR DIN SUFLET! Puncte+ coroana
Rezolvati va rog ,faceti U ,∩, \
A={x|x ∈R| x^2-x-6 >0}
B={x|x∈R| x^2-1>0}

Answer 1

la a
f(x)=x²-x-6
f(x)=0
x²-x-6=0
Δ=b²-4ac=(-1)²+2*6=1+24=25
x₁=$\frac{-b + \sqrt{d} }{2a}= \frac{1+ \sqrt{25} }{2} = \frac{1+5}{2} = \frac{6}{2} =3$
x₂=$\frac{-b- \sqrt{d} }{2a} = \frac{1- \sqrt{25} }{2} = \frac{1-5}{2} = \frac{-4}{2} =-2$
d-Δ

desenezi axa si notezi pe ea
x∈(-∞;-2)∪(3;+∞)

A=(-∞;-2)∪(3;+∞)

la b
x²-1≥0
x²≥1
x≥+-1
desenezi axa
x∈(-∞;-1]∪[1;+∞)
B=(-∞;-1]∪[1;+∞)

A∪B=B(scrie ce E scris la B)
A∩B=A(scrie ce e scris la A)
A/B=multime vida
B/A=(-2;-1]∪[1;3)={-1;1;2}