Răspuns :
a).2x la patrat-2x=10-2x
2x la patrat-2x=10-2x
2x la patrat -2x +2x=10. ii simplifici (tai) pe -2x si +2x si ramane:
2x la patrat=10
x la patrat=10\2=5
x= radical din 5
2x la patrat-2x=10-2x
2x la patrat -2x +2x=10. ii simplifici (tai) pe -2x si +2x si ramane:
2x la patrat=10
x la patrat=10\2=5
x= radical din 5
a)2x(x-1)=10-2x
2x²-2x=10-2x
Adunam 2x in ambii membri.
2x²=10
x²=5
|x|=√5
x∈{√5; -√5}
b)6x(5x+2)=12x
30x²+12x=12x
30x²=0
x²=0
x=0
c)12(x+1)²=(6+2√3)²
12(x+1)²=(36+12+24√3)
12(x+1)²=48+24√3
12(x+1)²=12(4+2√3)
(x+1)²=4+2√3
|x+1|=√(4+2√3)
|x+1|=√(4+√12)
Pentru a-l calcula pe 4+√12 folosim formula radicalilor compusi:
C=√(16-12)
C=√4
C=2
4+√12=√[(4+2)/2]+√[(4-2)/2]=√(6/2)+√(2/2)=√3+1
|x+1|=√3+1
x+1∈{√3+1; -√3-1}
x∈{√3; -√3-2}
2x²-2x=10-2x
Adunam 2x in ambii membri.
2x²=10
x²=5
|x|=√5
x∈{√5; -√5}
b)6x(5x+2)=12x
30x²+12x=12x
30x²=0
x²=0
x=0
c)12(x+1)²=(6+2√3)²
12(x+1)²=(36+12+24√3)
12(x+1)²=48+24√3
12(x+1)²=12(4+2√3)
(x+1)²=4+2√3
|x+1|=√(4+2√3)
|x+1|=√(4+√12)
Pentru a-l calcula pe 4+√12 folosim formula radicalilor compusi:
C=√(16-12)
C=√4
C=2
4+√12=√[(4+2)/2]+√[(4-2)/2]=√(6/2)+√(2/2)=√3+1
|x+1|=√3+1
x+1∈{√3+1; -√3-1}
x∈{√3; -√3-2}
