Question

упр 5,64 решите срочно 50 Б

Answer 1

Здравствуйте!

Вот ваше решение:

Первое уравнение:

$x^{3}-6x^{2} = 6-x\\x^{2}(x-6)=6-x\\x^{2}(x-6)(6-x)=0\\x^{2}(x-6)+x-6=0\\(x-6)(x^{2}+1)=0\\\\x-6=0\\x^{2}+1=0\\x = 6\\x^{2} = -1\\\\x=6$

Второе уравнение:

$y^{3}+3y^{2}  -4y-12=0\\y^{2}(y+3)-4(y+3)=0\\(y+3)(y^{2}-4)=0\\\\y+3=0\\ y^{2} -4=0 \\y = -3\\y= -2\\y = 2\\\\y_{1} = -3\\y_{2} = 2\\y_{3} = -2$

Третье уравнение:

$2x^{3}-x^{2} -18x+9=0\\x^{2}(2x-1)-9(2x-1)=0\\(2x-1)(x^{2}-9)=0\\\\2x-1=0\\x^{2} -9=0\\\\x = 0.5\\x= -3\\x= 3 \\\\x_{1} = 0.5\\x_{2} = -3\\x_{3} = 3$

Четвертое уравнение:

$4y^{3}-3y^{2} -4y+3=0\\y^{2}(4y-3)-(4y-3)=0\\(4y-3)(y^{2}-1)=0\\ \\4y-3= 0 \\y^{2}-1=0\\ \\y= 0.75\\y= -1\\y= 1\\\\y_{1} = -1\\y_{2}= 1\\y_{3} = 0.75$

Пятое уравнение:

$2x^{2} -x^{2} -32x+16=0\\x^{2}(2x-1)-16(2x-1)=0\\(2x-1)(x^{2} -16)=0\\\\2x-1=0\\x^{2} -16=0\\\\x = 0.5\\x = -4\\x= 4\\\\x_{1} = -4\\x_{2} = 0.5\\x_{3} = 4$

Шестое уравнение:

$(y+6)^{2} - (y+5)(y-5)=79\\y^{2} +12y+36-(y^{2} -25)=79\\y^{2} + 12y+36-y^{2} +25=79\\12y + 61 = 79\\12y = 79-61\\12y = 18\\y = 18 : 12\\y = 1.5$