Question

50 баллов!3 номера алгебра 7 класс

Answer 1

$572.\\a)\;3x^2+22x-16=0\\D=484+4\cdot3\cdot16=484+192=676=(26)^2\\x_1=\frac{-22-26}6=-8\\x_2=\frac{-22+26}6=\frac23\\3x^2+22x-16=3(x+8)(x-\frac23)=(x+8)(3x-2)\\\\b)\;4x^2-33x-27=0\\D=1089+4\cdot4\cdot27=1089+432=1521=(39)^2\\x_1=\frac{33-39}8=-\frac34\\x_2=\frac{33+39}8=9\\4x^2-33x-27=4(x+\frac34)(x-9)=(4x+1)(x-9)\\\\c)\;8x^2-19x-15=0\\D=361+4\cdot8\cdot15=361+480=841=(29)^2\\x_1=\frac{19-29}{16}=-\frac58\\x_2=\frac{19+29}{16}=3\\8x^2-19x-15=8(x+\frac58)(x-3)=(8x+5)(x-3)$

$d)\;6x^2-17x-28=0\\D=289+4\cdot6\cdot28=289+672=961=(31)^2\\x_1=\frac{17-31}{12}=-\frac76\\x_2=\frac{17+31}{12}=4\\6x^2-17x-28=6(x+\frac76)(x-4)=(6x+7)(x-4)\\\\573.\\a)\;35x^3-20x^2y-42xy+A=7x(5x^2-6y)-4y(5x^2-\frac{A}{4y})\\\frac{A}{4y}=6y\Rightarrow A=24y^2\\35x^3-20x^2y-42xy+A=35x^3-20x^2y-42xy+24y^2=\\=7x(5x^2-6y)-4y(5x^2-6y)=(7x-4y)(5x^2-6y)\\A=24y^2,\B=5x^2,\;C=6y$

$b)\;32m^3-A+32m-56n=4m(8m^2+8)-7n(\frac A{7n}+8)\\\frac A{7n}=8m^2\Rightarrow A=56m^2n\\32m^3-A+32m-56n=32m^3-56m^2n+32m-56n=\\=4m(8m^2+8)-7n(8m^2+8)=(8m^2+8)(4m-7n)\\A=56m^2n,\;B=4m,\;C=7n\\\\574.\\a)\;2y^3-18y^2+y-9=0\\2y^2(y-9)+(y-9)=0\\(2y^2+1)(y-9)=0\\\begin{cases}2y^2+1=0\\y-9=0\end{cases}\Rightarrow\begin{cases}2y^2=-1\;-\;DeucTB.\;KOPHEu\;HET\\y=9\end{cases}\\\\b)\;x^4-4x^3+8x^2-32x=0\\x^2(x^2-4x)+8(x^2-4x)=0\\(x^2+8)(x^2-4x)=0$

$\begin{cases}x^2+8=0\\x^2-4x=0\end{cases}\Rightarrow\begin{cases}x^2=-8\;-\;DeucTB.\;KOPHEu\;HET\\x(x-4)=0\end{cases}\Rightarrow\\\Rightarrow\begin{cases}x_1=0\\x_2=4\end{cases}$