<span>AC=h/sin30=30/0.5=60см...... АВ=h/sin75=30/((√2+√6)/4)=30√6-30√2......... BC=√AC²+AB²-2*AC*AB-cos45=√60²+(30√6-30√2)²-2*60*(30√6-30√2)*√2/2=√(14400-7200√3)
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2) (4x -y)² -(4x+y)² ? x=1 1/8 =( 1*8+1/)8 =19/8 b=-0,2.
(4x -y)² -(4x+y)² =(4x-y-(4x+y))(4x-y+4x+y) = -2y*8x = -16xy=-16*9/8*(-0,2) =
=18*0,2 =3,6.
или
(4x -y)² -(4x+y)² =(4x)² -2*(4x)*y +y²) -(16x² +8xy+y²) =16x² -8xy+y²-16x² -8xy-y²=
-16xy
3)( 2x-5)² - 2(7x-1)² =((2x)² -2*2x*5 +5²) - 2((7x)² -2*7x*1 +1²)=
4x² -20x+25 -2(49x² -14x ²+1)= 4x² -20x +25 -98x²+28x -2 =-94x²+8x+23.
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].