X - искомое число.
x/2 - x/3 = 0,5
3x - 2x = 3
x = 3
Проверка: 3/2 - 3/3 = 1,5 - 1 = 0,5
Ответ: число равно 3.
(x-4)(2x-1)=3x+8
2x^2+x-8x-4-3x-8=0
2x^2-10x-12=0
x^2-5x-6=0
D=√49=7
x1=6
x2=-1
1) sinx - (1 - sin^2(x)) - sin^2(x) = 0
sinx - 1 + sin^2(x) - sin^2(x) = 0
sinx = 1
x = 2πk, k∈Z
2) sinx = t ∈[-1;1]
6t^2 + t - 1 = 0, D=1+4*6 = 25
t1 = (-1-5)/12 = -6/12 = -1/2, sinx = -0.5, x = π/6 + 2πk и x = 5π/6 + 2πk, k∈Z
t2 = (-1+5)/12 = 4/12 = 1/3, sinx = 1/3, x = arcsin(1/3) + 2πk и x = π - arcsin(1/3) + 2πk, k∈Z
3) 1 - sin^2(x) - 4sinx + 3 = 0
-sin^2(x) - 4sinx + 4 = 0
sin^2(x) + 4sinx - 4 = 0
sinx = t ∈[-1;1]
t^2 + 4t - 4 = 0, D=16+16=32
t1 = (-4-√32)/2 < -1
t2 = (-4+√32)/2, x = arcsin((-4+√32)/2) + 2πk и x = π - arcsin((-4+√32)/2) + 2πk
4) sinx*(√3*sinx - 3cosx) = 0
sinx = 0, x = πk
tgx = √3, x = π/3 + πk
5) 2sin^2(x) - √3*2sinx*cosx = 0
2sinx*(sinx - √3*cosx) = 0
sinx = 0, x = πk
tgx = √3, x = π/3 + πk
4. А)1) (х-3)²-х(х+2,7)=9
2) x² - 6x + 9 - x²- 2,7x=9;
3) -8,7x=9-9;
4) -8,7x=0;
5) x=0;
Б)1) 9y²-25=0;
2) 3²y²-5²=0;
3) (3y-5)(3y+5)=0;
4) 3y-5=0;
5) 3y=5;
6) y=5/3;
7) y=1 2/3;
8) 3y+5=0;
9) 3y= -5;
10)y= -5/3;
11)y= -1 2/3;
5.
А) (x²+1)(x-1)(x+1)=(x²+1) (x²-1)=x⁴-1;
Б) (3a²-6b²)(3a²+6b²)=9a⁴-36b⁴;
Удачи :) !