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1) \(\left[\left(a+b\right)-c\right]^2=\left(a+b\right)^2-2c\left(a+b\right)+c^2\)
\(=\left(a^2+2ab+b^2\right)-2ac-2bc+c^2\)
\(=a^2+b^2+c^2+2ab-2ac-2bc\)
2)Phần này tg tự
3)\(\left(x+y+z\right)\left(x+y-z\right)=\left(x+y\right)^2-z^2=x^2+2xy+y^2-z^2\)
\(a^2+b^2=\left(a+b\right)^2-2ab=1^2-2\left(-3\right)=7\)
\(a^3+b^3=\left(a+b\right)^3-3ab\left(a+b\right)=1^3-3.\left(-3\right).1=10\)
Ta có: \(a+b=1\)
\(\Leftrightarrow\left(a+b\right)^2=1\)
\(\Leftrightarrow a^2+b^2+2ab=1\)
\(\Leftrightarrow a^2+b^2-2\cdot3=1\)
\(\Leftrightarrow a^2+b^2=1+6=7\)
Ta có: \(a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)\)
\(=7-\left(-3\right)\)
\(=7+3=10\)
a, (452 - 2.40.45 + 402) - 152
= ( 45 - 40 )2 - 152
= 52 - 152 = ( 5 - 15 )( 5 + 15 )
= -200
b, 13 . 4 . 13 .11 - 13 . 4 . 13 . 3 - 32
= 132 . 44 - 132 . 12 - 32
= 132 ( 44 -12 ) - 32
= 32 ( 132 - 1 )
= 32 . ( 13 - 1 )( 13 + 1 )
= 32 . 12 . 14
= 5376
\(45^2+40^2-15^2-80\cdot45\)
\(=\left(45^2-2\cdot45\cdot40+40^2\right)-15^2\)
\(=\left(45-40\right)^2-15^2\)
\(=15^2-15^2\)
\(=0\)
\(52\cdot143 -52\cdot39-8\cdot4\)
\(=7436-2028-32\)
\(=5408-32\)
\(=5440\)
C1
a) -7x(3x-2)=-21x^2+14x
b) 87^2+26.87+13^2=87^2+2.13.87+13^2=(87+13)^2=100^2
C2
a) (x-5)(x+5)
b)3x(x+5)-2(x+5)=(3x-2)(x+5)=0
\(\Rightarrow\left[\begin{array}{nghiempt}3x-2=0\\x+5=0\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}x=\frac{2}{3}\\x=-5\end{array}\right.\)
Vậy S={-5;2/3}
C3:
a)3x^3-2x^2+2=(x+1)(3x^2-5x-5)-3
b) Để A chia hết cho B=> x+1\(\inƯ\left(-3\right)\)
\(\Rightarrow\begin{cases}x+1=3\\x+1=-3\\x+1=1\\x+1=-1\end{cases}\)\(\Rightarrow\begin{cases}x=2\\x=-4\\x=0\\x=-2\end{cases}\)
a) 3x3-2x2+2 chia x+1= 3x2-5x+5 dư -3 b) -3 chia hết x+1 vậy chon x =2
1)
a) \(-7x\left(3x-2\right)\)
\(=-21x^2+14x\)
b) \(87^2+26.87+13^2\)
\(=87^2+2.87.13+13^2\)
\(=\left(87+13\right)^2\)
\(=100^2\)
\(=10000\)
2)
a) \(x^2-25\)
\(=x^2-5^2\)
\(=\left(x-5\right)\left(x+5\right)\)
b) \(3x\left(x+5\right)-2x-10=0\)
\(\Leftrightarrow3x\left(x+5\right)-\left(2x-10\right)=0\)
\(\Leftrightarrow3x\left(x+5\right)-2\left(x-5\right)=0\)
\(\Leftrightarrow\left(x+5\right)\left(3x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+5=0\\3x-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-5\\3x=2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=\dfrac{2}{3}\end{matrix}\right.\)
Vậy..........
3)
a) \(A:B=\left(3x^3-2x^2+2\right):\left(x+1\right)\)
Vậy \(\left(3x^3-2x^2+2\right):\left(x+1\right)=\left(3x^2-5x-5\right)+7\)
b)
Để \(A⋮B\Rightarrow7⋮\left(x+1\right)\)
\(\Rightarrow\left(x+1\right)\in U\left(7\right)=\left\{-1;1-7;7\right\}\)
Vì x là số nguyên nên x=0 ; x=6 thì \(A⋮B\)
Sửa đề: Cho \(a^2+b^2+c^2=m\)
Tính: \(A=\left(2a+2b-c\right)^2+\left(2b+2c-a\right)^2+\left(2c+2a-b\right)^2\)
Giải:
Ta có: \(\left(x+y-z\right)^2=\left(x+y\right)^2-2\left(x+y\right).z+z^2=x^2+y^2+z^2+2xy-2xz-2yz\)
Ứng dụng vào bài trên:
\(A=\left[\left(2a\right)^2+\left(2b\right)^2+c^2+2\left(2a\right)\left(2b\right)-2\left(2a\right)c-2\left(2b\right)c\right]\)
\(+\left[\left(2b\right)^2+\left(2c\right)^2+a^2+2\left(2b\right)\left(2c\right)-2\left(2b\right)a-2\left(2c\right)a\right]\)
\(+\left[\left(2c\right)^2+\left(2a\right)^2+b^2+2\left(2c\right)\left(2a\right)-2\left(2c\right)b-2\left(2a\right)b\right]\)
\(=4a^2+4b^2+c^2+8ab-4ac-4bc\)
\(+4b^2+4c^2+a^2+8bc-4ba-4ca\)
\(+4c^2+4a^2+b^2+8ca-4cb-4ab\)
\(=9a^2+9b^2+9c^2=9\left(a^2+b^2+c^2\right)\)
\(=9m\).
(90+1)2=902+2.90.1+12=8100+180+1=8281
HỌC TỐT!!