Question

Rezolvați următoarele ecuații :

Answer 1

a)√5x-1=x+1
CE:5X-1≥0⇒X≥1|5
X+1≥0⇒X≥-1
x∈(-1+∞]
(√5x-1)²=(x+1)²⇒
5x-1=x²+2x+1⇒x²-5x+2x+1+1=0⇒-x²-3x+2=0
a=1
b=-3
c=2
Δ=b²-4ac⇒(-3)²-4×1×⇒Δ=9-8⇒Δ=1
x1x2=-b-+√Δ|2a
x1=3+1|2⇒4|2⇒x1=2
x2=3-1|2⇒2|2⇒x2=1

2)∛x²-6x+9=1
se elimlna radicalul fiind ridicat la puterea a 3
(∛x²-6x+9)³=1³⇒x²-6x+9=1⇒x²-6x+8=0
a=1
b=-6
c=8
Δ=b²-4ac⇒Δ=(-6)²-4×1×8⇒36-32⇒Δ=4⇒√Δ=√4⇒Δ=2
x1x2=-b-+√Δ|2a⇒
x1=6+2|2⇒8|2⇒x1=4
x2=6-2|2⇒4|2⇒x2=2
succes