(7+у)²=7²+2*7*у+у²=49+14у+у²
3. a)
3ˣ⁺²-2*3ˣ⁺¹+3ˣ<12
3²*3ˣ-2*3*3ˣ+3ˣ<12
9*3ˣ-6*3ˣ+3ˣ<12
4*3ˣ<12
3ˣ<3¹
x<1.
3. b)
(log₀,₅x)²+3*log₀,₅x-4≤0 ОДЗ: x>0
log₀,₅x=t
t²+3t-4≤0
t²+3t-4=0 D=25
t₁=1 log₀,₅x=1 x₁=0,5
t₂=-4 log₀.₅x=-4 x₂=16
(t+4)(t-1)≤0
t∈[-4;1]
log₀,₅x≥-4 log₀,₅x≥log₀,₅16 x≤16
log₀,₅x≤1 log₀,₅x≤log0,5 x≥0,5 ⇒
x∈[0,5;16].
6х²+5mx+m²=0
a=6
b=5m
c=m²
D=b²-4ac = 25m² - 24m² = m²
x₁ = -b-√D / 2a = -5m-m / 12 = - m/2
x₂ = -b+√D / 2a = -5m+m / 12 = - m/3