решите уравнения
1) x^2-5= (x+5)(2x-1)
2) (2x+3)(3x+1)=11x+30
3)2x-(x+1)^2=3x^2-6
4) 6a^2-(a+2)^2= - 4(a-4)
5)x(7-6x)=(1-3x)(1+2x)
6)(5y+2)(y-3)= - 13(2+y)
1) x^2-5= (x+5)(2x-1)
2) (2x+3)(3x+1)=11x+30
3)2x-(x+1)^2=3x^2-6
4) 6a^2-(a+2)^2= - 4(a-4)
5)x(7-6x)=(1-3x)(1+2x)
6)(5y+2)(y-3)= - 13(2+y)
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Answers & Comments
x^2 - 5 = 2x^2 - x + 10x - 5
2x^2 - x^2 - x - 10x - 5 + 5 = 0
x^2 - 9x = 0
x * (x - 9) = 0
x = 0 или x = 9
(2x+3)(3x+1)=11x+30
6x^2 + 2x + 9x + 3 = 11x + 30
6x^2 + 11x - 11x = 30 - 3
6x^2 = 27
2x^2 = 9
x^2 = 9/2
x = 3/√2
2x-(x+1)^2=3x^2-6
2x - x^2 - 1 - 2x = 3x^2 - 6
3x^2 + x^2 = 5
4x^2 = 5
x^2 = 5/4
x = √5/2
6a^2-(a+2)^2= - 4(a-4)
6a^2 - a^2 - 4 - 4a = - 4a + 16
5a^2 = 20
a^2 = 4
a = 2
x(7-6x)=(1-3x)(1+2x)
7x - 6x^2 = 1 + 2x - 3x - 6x^2
7x - 2x + 3x = 1
8x = 1
x = 1/8
(5y+2)(y-3)= - 13(2+y)
5y^2 - 15y + 2y - 6 = - 26 - 13y
5y^2 - 13y + 13y = - 26 + 6
5y^2 = - 20
y^2 = - 4
y = решений нет, поскольку из отрицательного числа квадратный корень извлечь невозможно.