Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a: \(=1995^2-\left(1995^2-1\right)=1995^2-1995^2+1=1\)
b: \(=18^8-18^8+1=1\)
c: \(=\left(163+37\right)^2=200^2=40000\)
a)
\(x^4+1996x^2+1995x+1996\)
\(=\left(x^4-x\right)+\left(1996x^2+1996x+1996\right)\)
\(=x\left(x^3-1\right)+1996\left(x^2+x+1\right)\)
\(=x\left(x-1\right)\left(x^2+x+1\right)+1996\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left[x\left(x-1\right)+1996\right]\)
\(=\left(x^2+x+1\right)\left(x^2-x+1996\right)\)
b)
\(x^4+1997x^2+1996x+1997\)
\(=\left(x^4-x\right)+\left(1997x^2+1997x+1997\right)\)
\(=x\left(x^3-1\right)+1997\left(x^2+x+1\right)\)
\(=x\left(x-1\right)\left(x^2+x+1\right)+1997\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left[x\left(x-1\right)+1997\right]\)
\(=\left(x^2+x+1\right)\left(x^2-x+1997\right)\)
x4+1996x2+1995x+1996
=(x4_x)+(1996x2+1996x+1996)
=x(x3-1)+1996(x2+x+1)
=x(x-1)(x2+x+1)+1996(x2+x+1)
=(x2+x+1)((x2-1)+1996)
=(x2+x+1)((x+1)(x-1)+1996)
Câu 2 tương tự bạn nhé!
1)
a)
\(2x+5=20+3x\\ \Leftrightarrow2x+5-20-3x=0\\ \Leftrightarrow-x-15=0\\ \Rightarrow x=-15\)
b)
\(2.5y+1.5=2.7y-1.5c\cdot2t-\frac{3}{5}=\frac{2}{3}-t\\ \Leftrightarrow2.5y+1.5-2.7y+3ct+\frac{3}{5}-\frac{2}{3}+t=0\\ \Leftrightarrow-0.2y+\frac{43}{30}+3ct+t=0\)
2)
a)
\(\frac{5x-4}{2}=\frac{16x+1}{7}\\ \Leftrightarrow\frac{35x-28}{14}-\frac{32x+2}{14}=0\\ \Leftrightarrow\frac{35x-28-32x-2}{14}=0\\ \Leftrightarrow\frac{3x-30}{14}=0\\ \Rightarrow3x-30=0\\ \Rightarrow x=10\)
b)
\(\frac{12x+5}{3}=\frac{2x-7}{4}\\ \Leftrightarrow\frac{48x+20}{12}-\frac{6x-21}{14}=0\\ \Leftrightarrow\frac{48x+20-6x+21}{12}=0\\ \Leftrightarrow\frac{42x+41}{12}=0\\ \Rightarrow42x+41=0\\ \Rightarrow x=-\frac{41}{42}\)
3)
a)
\(\left(x-1\right)^2-9=0\\ \Leftrightarrow\left(x-1-3\right)\cdot\left(x-1+3\right)=0\\ \Leftrightarrow\left(x-4\right)\cdot\left(x+2\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-4=0\\x+2=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=4\\x=-2\end{matrix}\right.\)
\(F=\frac{1996^3-1}{1996^2+1997}=\frac{\left(1996-1\right)\left(1996^2+1996+1\right)}{1996^2+1997}=\frac{1995.\left(1996^2+1997\right)}{1996^2+1997}=1995\)
E = \(\frac{1995^3}{1995^2-1994}=\frac{1995^3+1-1}{1995^2-1994}=\frac{\left(1995+1\right)\left(1995^2-1995+1\right)-1}{1995^2-1994}\)
=\(\frac{1996\left(1995^2-1994\right)-1}{1995^2-1994}=1996-\frac{1}{1995^2-1994}\)
Vì \(1995^2-1994>0\) => \(\frac{1}{1995^2-1994}<1\) => \(-\frac{1}{1995^2-1994}>-1\) => \(1996-\frac{1}{1995^2-1994}>1996-1\)
HAy E > F
1) A=19952-1994.1996
=19952-(1995-1)(1995+1)
=19952-(19952-1)
=1
2) B=98.28-(184-1)(184+1)
=(9.2)8-[(184)2-1]
= 188-188+1
=1
3) C=1632+74.163+372
=1632+2.37.163+372
=1632+2.163.37+372
=(163+37)2.2
=80000
a/Viết đề mà cx sai đc nữa: \(\left(\frac{x+2}{98}+1\right)\left(\frac{x+3}{97}+1\right)=\left(\frac{x+4}{96}+1\right)\left(\frac{x+5}{95}+1\right)\)
\(\Leftrightarrow\frac{x+100}{98}.\frac{x+100}{97}-\frac{x+100}{96}.\frac{x+100}{95}=0\)
\(\Leftrightarrow\left(x+100\right)^2\left(\frac{1}{98.97}-\frac{1}{96.95}\right)=0\)
\(\Rightarrow x=-100\)
b/\(\Leftrightarrow\left(\frac{x+1}{1998}+1\right)+\left(\frac{x+2}{1997}+1\right)=\left(\frac{x+3}{1996}+1\right)+\left(\frac{x+4}{1995}+1\right)\)
\(\Leftrightarrow\frac{x+1999}{1998}+\frac{x+1999}{1997}-\frac{x+1999}{1996}-\frac{x+1999}{1995}=0\)
\(\Leftrightarrow\left(x+1999\right)\left(...\right)=0\Rightarrow x=-1999\)
b,\(\frac{x+1}{1998}+\frac{x+2}{1997}=\frac{x+3}{1996}+\frac{x+4}{1995}\)
=>\(\frac{x+1}{1998}+1\frac{x+2}{1997}+1=\frac{x+3}{1996}+1+\frac{x+4}{1995}+1\)
\(\Leftrightarrow\)\(\frac{x+1999}{1998}+\frac{x+1999}{1997}=\frac{x+1999}{1996}+\frac{x+1999}{1995}\)
\(\Leftrightarrow\)\(\frac{x+1999}{1998}+\frac{x+1999}{1997}-\frac{x+1999}{1996}-\frac{x+1999}{1995}\)=0
\(\Leftrightarrow\)\(\left(x+1999\right)\left(\frac{1}{1998}+\frac{1}{1997}-\frac{1}{1996}-\frac{1}{1995}\right)\)=0
\(\Leftrightarrow\)x+1999=0(Vì \(\frac{1}{1998}+\frac{1}{1997}-\frac{1}{1996}-\frac{1}{1995}\ne0\))
\(\Leftrightarrow\)x=-1999
Vậy x=-1999
1001\(^2\)=(1000+1)\(^2\)=1000\(^2\)-2.1000+1
=1000000-2000+1
=tự tính
bài a đơn giản lắm:
99.101 = (100 - 1)(100 + 1)
= 1002 - 1 ( 12 thì tất nhiên = 1 rồi)
= 9999 ( số đẹp ghê!)
c) 19952 - 1994.1996 = 19952 - (1995 - 1) (1995 + 1)
= 19952 - (19952 - 1)
= 19952 - 19952 + 1
= 1