Question

Determinati mulțimea solutiilor fiecărei ecuatii:
a) 2x la a doua + 5 =13
b)8x la a doua -2 =0
c)6 la a doua -3 =0
d)16x la a doua +15 =14

Answer 1

a)
2x²+5=13
2x²+5-13=0
2x²-8=0
2(x²-4)=0
x²-4=0
x²=4⇒x∈{2,-2}

b)
8x²-2=0
2(4x²-1)=0
4x²-1=0
4x²=1
x²=1/4⇔x∈{1/2,-1/2}

c)
6x²-3=0
3(2x²-1)=0
2x²-1=0
2x²=1
x²=1/2⇒x∈{1/√2,-1/√2}

d)
16x²+15=14
16x²+15-14=0
16x²+1=0
16x²=-1⇒ecuatia nu are solutii

Answer 2

a) 2x²+5=13
2x²=13-5
2x²= 8
x²=8:2
x²=4
x=√4
x =± 2
S ={-2,2}
b) 8x²=0
x=0
S={0}
c) 6x²-3=0
6x²=3
x²= 3/6
x²= 1/2
x=√1/2
x= ±√2/2
S=-√2/2,√2/2}
d) 16x²+15=14
16x²=14 -15
16x²=-1
S= ¢