e, (30x³+120x)-(18x²y+72y)

=30x(x²+4)-18y(x²+4)

=(x²+4)(30x-18y)

f,(70x+20xy)-(84y+24y²)

= 10x(7+2y)-12y(7+2y)

=)7+2y)(10x-12y)

e) 30x³ - 18x²y - 72y +120x

= 6 ( 5x³ - 3x²y - 12y + 20x )

= 6 ( x² (5x - 3y) + 4 (5x - 3y)

= 6 (x²+4)(5x-3y)

f) 70x - 84y + 20xy -24y²

= 2 (35x - 42y + 10xy - 12y²)

= 2 ( 7(5x - 6y) + 2y(5x - 6y))

= 2(5x-6y)(7+2y)

\(30x^3-18x^2y-72y+120x\)

= \(6\left(5x^3-3x^2y-12y+20x\right)\)

= \(6\left[x^2\left(5x-3y\right)+4\left(5x-3y\right)\right]\)

= \(6\left(x^2+4\right)\left(5x-3y\right)\)

\(70x-84y+20xy-24y^2\)

= \(2\left(35x-42y+10xy-12y^2\right)\)

= \(2\left[7\left(5x-6y\right)+2y\left(5x-6y\right)\right]\)

= \(2\left(5x-6y\right)\left(7+2y\right)\)

\(B=\left|5x-2\right|+\left|5x-3\right|\)

\(=\left|5x-2\right|+\left|3-5x\right|\)

=>B>=|5x-2+3-5x|=1

Dấu = xảy ra khi (5x-2)(5x-3)<=0

=>2/5<=x<=3/5

Giúp mk vs các pạn ơi!!! Mk cần gấp!!!

mình mới học lớp 6 xin lỗi nha

\(P=\sqrt[]{9x^2-6x+1}+\sqrt[]{25-30x+9x^2}\)

\(\Leftrightarrow P=\sqrt[]{\left(3x-1\right)^2}+\sqrt[]{\left(5-3x\right)^2}\)

\(\Leftrightarrow P=\left|3x-1\right|+\left|5-3x\right|\)

\(\Leftrightarrow P=\left|3x-1\right|+\left|5-3x\right|\ge\left|3x-1+5-3x\right|=4\)

Vậy \(GTNN\left(P\right)=4\)

P = 4

\(A=x^2-4xy+7y^2+10x-24y+30\\ =\left(x^2-4xy+4y^2\right)+10\left(x-y\right)+25+\left(3y^2-14y+\dfrac{49}{3}\right)-\dfrac{34}{3}\\ =\left(x-2y+5\right)^2+3\left(y-\dfrac{7}{3}\right)^2-\dfrac{34}{5}\)

Với mọi x;y thì \(\left(x-2y+5\right)^2\ge0;3\left(y-\dfrac{7}{3}\right)^2\ge0\)

Do đó:\(A\ge-\dfrac{34}{5}\)

Để \(A=-\dfrac{34}{5}\) thì:

\(\left[{}\begin{matrix}\left(x-2y+5\right)^2=0\\\left(y-\dfrac{7}{3}\right)^2=0\\\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-2y=-5\\y=\dfrac{7}{3}\\\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-5+\dfrac{2.7}{3}=-\dfrac{1}{3}\\y=\dfrac{7}{3}\\\end{matrix}\right.\)

Vậy...

Nguyễn Thị Hồng Nhung, Akai Haruma, Trần Hoàng Nghĩa, Trần Thiên Kim, Phạm Hoàng Giang, Nhật Hạ, DƯƠNG PHAN KHÁNH DƯƠNG, Toshiro Kiyoshi, Ribi Nkok Ngok, ...

Các pạn ơi, giúp mk vs!!! Toshiro Kiyoshi, Trần Hoàng Nghĩa, Nguyễn Thị Hồng Nhung, ...