a₂²=a₁·a₃
a)
a₁=1
a₂=x
a₃=1 9/16
x²=1·1 9/16
x²=1 9/16
x²-25/16=0
(x-5/4)(x+5/4)=0
x-5/4=0 ∨ x+5/4=0
x₁=5/4 ∨ x₂=-5/4
b)
a₁=x
a₂=4
a₃=16/3
4²=x·16/3
16=x·16/3
16/3x=16 |:16/3
x=3
c)
a₁=1/9
a₂=x-1
a₃=4
(x-1)²=1/9·4 |·9
9(x-1)²=4
9x²-18x+9=4
9x²-18x+5=0
Δ=(-18)²-4·9·5
Δ=324-180
Δ=144
√Δ=√144=12
x₁=(18-12)/(2·9)=6/18=1/3
x₂=(18+12)/(2·9)=30/18=5/3=1 2/3
d)
a₁=2(x+1)
x₂=x+1
x₃=x-1
(x+1)²=2(x+1)·(x-1)
x²+2x+1=2x²-2
x²+2x+1-2x²+2=0
x²-2x-3=0
Δ=(-2)²-4·1·(-3)
Δ=4+12
Δ=16
√Δ=√16=4
x₁=(2-4)/(2·1)=-2/2=-1
x₂=(2+4)/(2·1)=6/2=3
e)
a₁=x+4
a₂=5x+2
a₃=16x+1
(5x+2)²=(x+4)(16x+1)
25x²+20x+4=16x²+x+64x+4
25x²+20x=16x²+65x
25x²+20x-16x²-65x=0
25x²-16x²+20x-65x=0
9x²-45x=0
9x(x-5)=0 |:9
x(x-5)=0
x₁=0 ∨ x-5=0
x₂=5
