X² - 2x - 35 = 0
По обратной теореме Виета:
x₁ + x₂ = 2
x₁*x₂ = -35
x₁ = 7
x₂ = -5
Ответ: x = -5; 7.
2) x³ - 9 = x - 9x²
x³ + 9x² - x - 9 = 0
x²(x + 9) - (x + 9) = 0
(x² - 1)(x + 9) = 0
Произведение множителей тогда равно нулю, когда любой из множителей равен нулю:
x² - 1 = 0 и x + 9 = 0
x = -1 и 1 и x = -9
Ответ: x = -9; -1; 1.
1273. 1) log4(sin(пи/4)); 2) log10(tg(пи/4)); 3) log8(sin(3пи/4))
4) log2(cos(пи/3)); 5) log3(1) -log4(tg(пи/4))*log5(cos(0)).
Решение:
1) log4(sin(пи/4)) = log2²(1/√2) = (1/2)log2(1/2^(1/2))= (1/2)log2(2^(-1/2))=
= (1/2)*(-1/2)log2(2) = -1/4
2) log10(tg(пи/4)) = log10(1) = 0
3) log8(sin(3пи/4)) = log2³(sin(пи/2+пи/4)) =(1/3)log2(cos(пи/4))=
=(1/3)log2(1/√2) = (1/3)log2(1/2^(1/2))= (1/3)log2(2^(-1/2))=(1/3)*(-1/2)log2(2) = -1/6
4) log2(cos(пи/3)) = log2(1/2) = log2(2^(-1)) = -1*log2(2) = -1
5) log3(1) - log4(tg(пи/4))*log5(cos(0)) = 0 - log4(1)*log5(1) = -0*0 = 0
Ответ: 1) -1/4; 2) 0; 3) -1/6; 4) -1; 5) 0.