<span>log₈²x+2*log₈x=(1/2)^log₀,₅3 ОДЗ: x>0
log</span>₈²x+2*log₈x=(0,5)^log₀,₅3
log₈²x+2*log₈x=3
log₈²x+2*log₈x-3=0
Пусть log₈x=t ⇒
t²+2t-3=0 D=16
t₁=1 ⇒ log₈x=1 x₁=8¹=8.
t₂=-3 ⇒ log₈x=-3 x₂=8⁻³=1/512.
Ответ: x₁=8 x₂=1/512.
sin⁴α-cos⁴α+cos²α=(sin²α-cos²α)(sin²α+cos²α)+cos²α=
=(sin²α-cos²α)*1+cos²α=sin²α-cos²α+cos²α=sin²α.
4)
x⁴ + 3x² - 70 = 0
(x²)² + 3x² - 70 = 0
замена: х² = t
t² + 3t - 70 = 0
D = 3² - 4*1*(-70) = 9 + 280 = 289 = 17²
D>0 - два корня уравнения
t₁ = ( - 3 - 17)/(2*1) = -20/2 = - 10 не удовл. ( т.к. х²≥0)
t₂ = ( - 3 + 17)/(2*1) = 14/2 = 7
х² = 7
х₁ = √7
х₂ = - √7
5)
9х⁴ - 10х² + 1 = 0
замена х² = t
9t² - 10t + 1 = 0
D = (-10)² - 4*9*1 = 100 - 36 = 64 = 8² ; D>0
t₁ = ( - (-10) - 8)/(2*9) = (10-8)/18 = 2/18 = 1/9
t₂ = ( - (-10) + 8)/(2*9) = (10+8)/18 = 18/18 = 1
x² = 1/9
x₁ = √(1/9)
x₁ = 1/3
x₂ = - √(1/9)
x₂ = - 1/3
x² = 1
x₃ = 1
x₄ = - 1
0.36 - x^2 = 0
x^2 = 0.36
x = 0.6 и -0.6
1)(3x+7)*(4x-1)=(6x-3)*(2x+6)
12x²-3x+28x-7=12x²+36x-6x-18
-5x=-11|:(-5)
x=2,2
Ответ:2,2.
2)(5x+7)*(2x-8)=(10x-8)*(x+7)
10x²-40x+14x-56=10x²+70x-8x-56
-88x=0
x=0
3)(7x-1)*(x+8)=(4+7x)*(x+4)
7x²+56x-x-8=4x+16+7x²+28x
23x=24|:23
x=
148
а) 27, 9, 3, 1, -3, -9
б) 1/2, 2/3, 3/4, 4/5, 5/6
в) 103, 95, 87, 79, 71
