Решите уравнения 1)4^(2x) - 7 * 4^x + 16 = 0 2)2^(2x + 1) + 2^(x + 2) - 16 = 0 3)2*4^2x + 8 = 17 4)2 * 16^x - 7 * 4^x - 4 = 0 5)4^x + 6 = 4 4^(1/2 - x/2) 6)2^2x - 6 * 2^x + 8 = 0 7)4^x - 5 * 2^x + 4 = 0 8)9^(x+1) + 3^(x+2) - 18 = 0 9)25^x - 24 * 5^(x-1) - 5^(log5 3) + 2 = 0 10)7^(x-2) + 38 * 3^x = 7^(x+1)
t² - 7t + 16 = 0
D= 49-64 <0
корней нет.
2)
2t² + 4t - 16=0
t² + 2t - 8 = 0
D₁ = 1+8=9
t₁ = 2
t₂ = -4 не удов. усл. t>0
x=1
3)
2x= log₄4.5
x = log₁₆4.5
4)
2t² - 7t - 4=0
D = 49+32=81
t₁ = 4
t₂ = -1/2 не удов. усл. t>0
x=1
5)
t² + 3t = 4
t² + 3t - 4 = 0
t₁ = 1
t₂ = -4 не удов. усл.t>0
x=0
6)
t² - 6t + 8 = 0
D₁ = 9-8 = 1
t₁ = 4
t₂ = 2
x=2
x=1
7)
t² - 5t + 4= 0
t₁ = 1
t₂ = 4
x=0
x=2
8)
9t² + 9t - 18 = 0
t₁ = 1
t₁ = -2 не удов.
x= 0
9)
5*
5t² - 24t - 5 =0
D₁ = 144+25 = 169
t₁ = 5
t₂ = -1/5 не удов.
x= 1
10)
x = 2