Task/27370678
------------------
Один из корней уравнения x² - 6x+q=0 равен 10. Найдите другой корень и свободный член q .
--------------
x₁=10 корень ,следовательно 10² - 6*10 +q = 0 ⇒ q = - 40 .
* * * x² - 6x - 40 =0 ; x₁,₂ = 3 ±√(3²+40) = 3 ± 7 * * *
x₁*x₂ = q ⇔ 10*x₂ = - 40 ⇒ x₂ = -40 /10 = - 4 .
по другому
Теореме Виета { x₁+x₂ = 6 , { 10+x₂ = 6 , { x₂ = -4 ,
{ x₁*x₂ = q . ⇔ { 10* x₂ =q . ⇔ {-40 = q .
ответ : - 4 ; - 40. * * * x₂ = -4 , q = -40 . * * *
1) sinx = -1/2;
x = (-1)^(n+1)* arcsin(|-1/2|) + pi*n;
x = (-1)^(n+1)* pi/6) + pi*n; n ∈ Z
n = 0; x = -pi/6 ∉[0;3p]
n = 1; x = pi/6 + pi = 7pi/6 ∈<span>[0;3p]
</span>n = 2; x = -pi/6 + 2pi = 11pi/6 ∈<span>[0;3p]
</span>n = 3; x = pi/6 + 3pi ∉<span>[0;3p]
</span>Ответ: x = 7pi/6 ∪ x = 11pi/6
2) sinx = 1/2;
x = (-1)^(n)* arcsin1/2) + pi*n;
x = (-1)^(n)* pi/6)+ pi*n; n ∈ Z
n = -1; x = -pi/6 - pi ∉ [-p/2;3p/2]
n = 0; x = pi/6 ∈[-p/2;3p/2]
n = 1; x = -pi/6 + pi = 5pi/6 ∈[-p/2;3p/2]
n = 2; x = pi/6 + 2pi ∉[-p/2;3p/2]
Ответ: x = pi/6 ∪ x = 5pi/6
3) sinx = -√2/2;
x = (-1)^(n+1)* arcsin(|-√2/2|) + pi*n;
x = (-1)^(n+1)* pi/4) + pi*n; n ∈ Z
n = -4; x = -pi/4 - 4pi ∉[-3p;0]
n = -3; x = pi/4 - 3pi = -11pi/4 ∈[-3p;0]
n = -2; x = -pi/4 -2pi = -9pi/4 ∈[-3p;0]
n = -1; x = pi/4 - pi = - 3pi/4 ∈[-3p;0]
n = 0; x = -pi/4 ∈[-3p;0]
n = 1; x = pi/4 + pi ∉[-3p;0]
Ответ: x = -11pi/4 ∪ x = -9pi/4 ∪ x = pi/4 - pi ∪ x = -pi/4
4) sinx = √2/2;
x = (-1)^(n)* arcsin(√2/2) + pi*n;
x = (-1)^(n)* pi/4)+ pi*n; n ∈ Z
n = -2; x = pi/4 - 2pi = -7pi/4 ∉[-3p/2;5p/2]
n = -1; x = -pi/4 - pi = - 5pi/4 ∈[-3p/2;5p/2]
n = 0; x = pi/4 ∈[-3p/2;5p/2]
n = 1; x = -pi/4 + pi = 3pi/4 ∈<span>[-3p/2;5p/2]
</span>n = 2; x = pi/4 + 2pi = 9pi/4 ∈<span>[-3p/2;5p/2]
</span>n = 3; x = -pi/4 + 3pi ∉[-3p/2;5p/2]
Ответ: x = -5pi/4 ∪ x = pi/4 ∪ x = 3pi/4 ∪ x = 9pi/4
5) sinx = -√3/2;
x = (-1)^(n+1)* arcsin(|-√3/2|) + pi*n;
x = (-1)^(n+1)* pi/3) + pi*n; n ∈ Z
n = -2; x = -pi/3 - 2pi ∉[-2p;2p]
n = -1; x = pi/3 - pi = -2pi/3;
n = 0; x = -pi/3 ∈[-2p;2p]
n = 1; x = pi/3 + pi = 4pi/3 ∈[-2p;2p]
n = 2; x = -pi/3 + 2pi = 5pi/3 ∈[-2p;2p]
n = 3; x = pi/3 + 3pi ∉[-2p;2p]
Ответ: x = -2pi/3 ∪ x = -pi/3 ∪ x =4pi/3 ∪ x = 5pi/3
Вот подробное решение до дроби
