HOC24
Lớp học
Môn học
Chủ đề / Chương
Bài học
a) \(x^2-2xy-4z^2+y^2\)
\(\Leftrightarrow\left(x^2-2xy+y^2\right)-\left(2z\right)^2\)
\(\Leftrightarrow\left(x-y\right)^2-\left(2z\right)^2\)
\(\Leftrightarrow\left[\left(x-y\right)+2z\right]\left[\left(x-y\right)-2z\right]\)
\(\Leftrightarrow\left(x-y+2z\right)\left(x-y-2z\right)\)
Tại x=6, y=-4, z=45
\(\left[6-\left(-4\right)+2.45\right]\left[6-\left(-4\right)-2.45\right]=100.\left(-80\right)=-8000\)
b) \(3\left(x-3\right)\left(x+7\right)+\left(x-4\right)^2+48\)
\(\Leftrightarrow3\left(x^2+7x-3x-21\right)+\left(x^2-4x+4\right)+48\) \(\Leftrightarrow3x^2+21x-9x-63+x^2-4x+4+48\)
\(\Leftrightarrow4x^2+8x-11\)
Tại x=0,5 ta có:
\(4.\left(0,5\right)^2+8.0,5-11=-6\)
a) 5x(x-2000)-x+2000=0
5x(x-2000)-(x-2000)=0
(x-2000)(5x-1)=0
\(\Leftrightarrow\) x-2000=0 hoặc 5x-1=0
\(\Leftrightarrow\) x=2000 hoặc x=\(\dfrac{1}{5}\)
b) \(x^3-13x=0\)
\(x\left(x^2-13\right)=0\)
\(\Leftrightarrow x=0\) hoặc \(x^2-13=0\)
\(\Leftrightarrow x=0\) hoặc \(x=13\) hoặc \(x=-13\)
a) 85.12,7+5,3.12,7
=12,7(85+5,3)=1146,81
b) 52.143-52.39-8.26
=52.(143-39)-208
= 5200
=
a) 5x-20y=5(x-4y)
b) 5x(x-1)-3x(x-1)
= (x-1)(5x-3x)
c) x(x+y)-5x-5y
=x(x+y)-5(x+y)
=(x+y)(x-5)
a) \(x^2+xy+x\)
\(\Leftrightarrow x\left(x+y+1\right)\)
Tại x=77 và y=22 có:
\(\Leftrightarrow77\left(77+22+1\right)\)
\(=7700\)
b) \(x\left(x-y\right)+y\left(y-x\right)\)
\(\Leftrightarrow\left(x-y\right)\left(x+y\right)\)
\(\Leftrightarrow x^2-y^2\)
Tại x=53 và y=3, ta có:
\(53^2-3^2=2800\)
a) \(x+5x^2=0\)
\(x\left(1+5x\right)=0\)
\(\Leftrightarrow x=0\) hoặc \(1+5x=0\)
\(\Leftrightarrow x=0\) hoặc \(x=\dfrac{-1}{5}\)
b) \(x+1=\left(x+1\right)^2\)
\(\Leftrightarrow x+1-\left(x+1\right)^2=0\)
\(\Leftrightarrow\left(x+1\right)\left[1-\left(x+1\right)\right]=0\)
\(\Leftrightarrow\left(x+1\right)\left(1-x-1\right)=0\)
\(\Leftrightarrow\left(x+1\right)-x=0\)
\(\Leftrightarrow x+1=0\) hoặc \(-x=0\)
\(\Leftrightarrow x=-1\) hoặc \(x=0\)
a) \(\left(a+b\right)\left(a^2-ab+b^2\right)+\left(a-b\right)\left(a^2+ab+b^2\right)=2a^3\)
\(=a^3+b^3+a^3-b^3\)
\(=2a^3\)
b) \(a^3+b^3=\left(a+b\right)\left[\left(a-b\right)^2+ab\right]\)
\(\left(a+b\right)\left[\left(a^2-2ab+b^2\right)+ab\right]\)
\(\left(a+b\right)\left(a^2-2ab+b^2+ab\right)\)
\(\left(a+b\right)\left(a^2-ab+b^2\right)\)
\(a^3+b^3\)