Question

[Lê Chấn Long]

em đang gấp, mn giúp em sớm đc k ạ, em cảm ơn

Answer 1

[Nguyễn Huy Tú]

Bài 2 : 

a, \(x^2-5x=0\Leftrightarrow x\left(x-5\right)=0\Leftrightarrow x=0;x=5\)

b, \(4x^2-1-\left(2x+1\right)=0\Leftrightarrow\left(2x-1\right)\left(2x+1\right)-\left(2x+1\right)=0\)

\(\Leftrightarrow2\left(2x+1\right)\left(x-1\right)=0\Leftrightarrow x=-\frac{1}{2};x=1\)

c, \(x^2-7x+10=0\Leftrightarrow x^2-5x-2x+10=0\Leftrightarrow x\left(x-2\right)-5\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-5\right)\left(x-2\right)=0\Leftrightarrow x=2;x=5\)

d, \(\left(2x-3\right)^2-49=0\Leftrightarrow\left(2x-10\right)\left(2x+4\right)=0\Leftrightarrow x=-2;x=5\)

e, \(2x\left(x-5\right)-7\left(5-x\right)=0\Leftrightarrow\left(2x+7\right)\left(x-5\right)=0\Leftrightarrow x=-\frac{7}{2};x=5\)

f, \(x^2-3x-10=0\Leftrightarrow x^2+2x-5x-10=0\Leftrightarrow x\left(x+2\right)-5\left(x+2\right)=0\)

\(\Leftrightarrow\left(x-5\right)\left(x+2\right)=0\Leftrightarrow x=-2;x=5\)

g, \(x-2^3+2x+1^3-9x+1^3=-16\)đề này anh nghĩ ko đúng lắm nhé, nếu đề là : 

Ps : \(\left(x-2\right)^3+\left(2x+1\right)^3-\left(9x+1\right)^3=-16\)thì cứ khai triển ra em nhé, nhưng khá dài :))

\(\Leftrightarrow x-8+2x+1-9x+1=-16\Leftrightarrow-6x=-10\Leftrightarrow x=\frac{5}{3}\)

h, \(4x^2-25+\left(2x+5\right)^2=0\Leftrightarrow\left(2x-5\right)\left(2x+5\right)+\left(2x+5\right)^2=0\)

\(\Leftrightarrow\left(2x+5\right)\left(2x-5+2x+5\right)=0\Leftrightarrow4x\left(2x+5\right)=0\Leftrightarrow x=-\frac{5}{2};x=0\)

Answer 2

[Nguyễn Huy Tú]

Bài 1 : 

a, \(x^2-xy-6x+6y=x\left(x-y\right)-6\left(x-y\right)=\left(x-6\right)\left(x-y\right)\)

b, \(x^2+6x+9-y^2=\left(x+3\right)^2-y^2=\left(x+3-y\right)\left(x+3+y\right)\)

c, \(x^3+y^3+2x+2y=\left(x+y\right)\left(x^2-xy+y^2\right)+2\left(x+y\right)=\left(x+y\right)\left(x^2-xy+y^2+2\right)\)

d, \(x^2+4y^2-4xy-4=\left(x-2y\right)^2-4=\left(x-2y-2\right)\left(x-2y+2\right)\)

e, \(x^3-4x^2+4x=x\left(x^2-4x+4\right)=x\left(x-2\right)^2\)

f, \(5x^2\left(x-2y\right)-15x\left(x-2y\right)=\left(5x^2-15x\right)\left(x-2y\right)=5x\left(x-3\right)\left(x-2y\right)\)

g, \(x^2-y^2-6y-9=x^2-\left(y+3\right)^2=\left(x-y-3\right)\left(x+y+3\right)\)

h, \(3x^2+x-4=3x^2+4x-3x-4=3x\left(x-1\right)+4\left(x-1\right)=\left(3x+4\right)\left(x-1\right)\)