A²-2a+18-9a=a(a-2)-9(a-2)=(a-2)(a-9)
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a^5b²+27a²b^5=a²b²(a³+27b³)=a²b²(a+3b)(a²-3ab+9b²)
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(3x+1)(x-1)-(3x-1)(3x+1)=(3x+1)(x-1-3x+1)=(3x+1)(-2x)
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(2a-3b)²-2(a+b)²=(2a-3b-√2a-√2b)(2a-3b+√2a+√2b)
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(4a+1)²(4a-1)²=(16a²+1)²-64a²
(16a²+1)-64a²=(16a²+1-8a)(16a²+1+8a)=((4a-1)²(4a+1)²
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64x²-48x-25y²-30y=(8x-5y)(8x+5y)-6(8x+5y)=(8x+5y)(8x-5y-6)
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18a²+24a+8-200b²=2(9a²+12a+4)-2*100b²=2(3a+2)²-2*100b²=
=2(3a+2-10b)(3a+2+10b)
4) А, В - больше 0, меньше 1, С - 1, D - 0
Х×(2х+13) = 0
либо х = 0 либо 2х+13 = 0 х = - 13/2 = - 6.5
ответ: либо х = 0 либо х = - 6.5
Решение
<span>3^x + 8*3^(-x) </span>≥ <span>9
</span>3^(2x) - 9*(3^x) + 8 ≥ 0
3^x = t
t² - 9t + 8 = 0
t₁ = 1
t₂ = 8
1) 3^x = 1
3^x = 3°
x₁ = 0
2) 3^x = 8
log₃ (3^x) = log₃ 8
x₂ = log₃ 8