Giúp mk với tối nay 6h nộp rồi
Bài 1: Tìm x, biết
A) 4x-7=(2x+5)+x
B) (3x-5)+8=(2x-1)-100
Bài2: Rút gọn
A= (-a+b) -(b+c-a)+(c-a)
B= -(-a+b+c)+(b+c-1)
C=(b-c+6)-(7-a+b)+c
K
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15 tháng 11 2021
\(a,=\dfrac{x^4\left(x-2\right)+2x^2\left(x-2\right)-3\left(x-2\right)}{x+4}\\ =\dfrac{\left(x-2\right)\left(x^4+2x^2-3\right)}{x+4}\\ =\dfrac{\left(x-2\right)\left(x^4-x^2+3x^2-3\right)}{x+4}\\ =\dfrac{\left(x-2\right)\left(x-1\right)\left(x^2+3\right)}{x+4}\)
\(b,=\dfrac{x^4-3x^2-x^2+3}{x^4-x^2+7x^2-7}=\dfrac{\left(x^2-3\right)\left(x^2-1\right)}{\left(x^2+7\right)\left(x^2-1\right)}=\dfrac{x^2-3}{x^2+7}\\ c,=\dfrac{\left(x^3-1\right)\left(x+1\right)}{x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)}\\ =\dfrac{\left(x-1\right)\left(x^2+x+1\right)\left(x+1\right)}{\left(x^2+1\right)\left(x^2+x+1\right)}=\dfrac{x^2-1}{x^2+1}\)
15 tháng 11 2021
Bài 1:
Ta có: \(a^3+b^3+c^3=3abc\)
\(\Leftrightarrow\left(a^3+3a^2b+3ab^2+b^3\right)+c^3-3a^2b-3ab^2-3abc=0\)
\(\Leftrightarrow\left(a+b\right)^3+c^3-3ab\left(a+b+c\right)=0\)
\(\Leftrightarrow\left(a+b+c\right)\left[\left(a+b\right)^2-\left(a+b\right)c+c^2\right]-3ab\left(a+b+c\right)=0\)
\(\Leftrightarrow\left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ac\right)=0\)
\(\Leftrightarrow a^2+b^2+c^2-ab-bc-ac=0\left(do.a+b+c\ne0\right)\)
\(\Leftrightarrow2\left(a^2+b^2+c^2-ab-bc-ac\right)=0\)
\(\Leftrightarrow\left(a-b\right)^2+\left(b-c\right)^2+\left(a-c\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(a-b\right)^2=0\\\left(b-c\right)^2=0\\\left(a-c\right)^2=0\end{matrix}\right.\)\(\Leftrightarrow a=b=c\)
\(M=\dfrac{a^2+b^2+c^2}{\left(a+b+c\right)^2}=\dfrac{3a^2}{\left(3a\right)^2}=\dfrac{3a^2}{9a^2}=\dfrac{1}{3}\)
15 tháng 11 2021
Bài 2:
a) \(=\dfrac{x\left(x^2+x-6\right)}{x\left(x^2-4\right)}=\dfrac{x\left(x-2\right)\left(x+3\right)}{x\left(x-2\right)\left(x+2\right)}=\dfrac{x+3}{x+2}\)
b) \(=\dfrac{x\left(x+1\right)+7\left(x+1\right)}{x\left(x^2+2x+1\right)}=\dfrac{\left(x+1\right)\left(x+7\right)}{x\left(x+1\right)^2}=\dfrac{x+7}{x\left(x+1\right)}=\dfrac{x+7}{x^2+x}\)
10 tháng 1 2021
a) Ta có: \(\left|x+7\right|-\left(-8\right)=-25+73\)
\(\Leftrightarrow\left|x+7\right|+8=48\)
\(\Leftrightarrow\left|x+7\right|=40\)
\(\Leftrightarrow\left[{}\begin{matrix}x+7=40\\x+7=-40\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=33\\x=-47\end{matrix}\right.\)
Vậy: \(x\in\left\{33;-47\right\}\)
c) Ta có: \(-\left(a-b\right)+\left(b-c\right)-\left(a-c\right)=2b-2a\)
\(\Leftrightarrow-a+b+b-c-a+c=2b-2a\)
\(\Leftrightarrow-2a+2b-2b+2a=0\)
\(\Leftrightarrow0a+0b=0\)(luôn đúng)
Vậy: \(\left\{{}\begin{matrix}a\in Z\\b\in Z\end{matrix}\right.\)
d) Ta có: \(-\left(-a+b+c\right)+\left(b+c-1\right)=-\left(b-a\right)-\left(1-b\right)\)
\(\Leftrightarrow a-b-c+b+c-1=-b+a-1+b\)
\(\Leftrightarrow a-1=a-1\)(luôn đúng)
Vậy: \(\left\{{}\begin{matrix}a\in Z\\b\in Z\\c\in Z\end{matrix}\right.\)
e) Ta có: \(-\left(-a+b+c\right)+\left(b-c+6\right)=a+6\)
\(\Leftrightarrow a-b-c+b-c+6=a+6\)
\(\Leftrightarrow a+6-2c-a-6=0\)
\(\Leftrightarrow-2c=0\)
hay c=0
Vậy: \(\left\{{}\begin{matrix}a\in Z\\b\in Z\\c=0\end{matrix}\right.\)
1)
a) 4x - 7 = (2x + 5) + x
4x - 7 = 2x + 5 + x
4x - 2x - x = 5 + 7
=> x = 12
b) (3x - 5) + 8 = (2x - 1) - 100
3x - 5 + 8 = 2x - 1 - 100
3x - 2x = -1 - 100 + 5 + 8
=> x = -88
2)
A = (-a+b) - (b+c-a)+(c-a)
A = -a + b - b -c + a + c - a
A = 0
B = -(-a+b+c) + (b+c-1)
B = a - b - c + b + c - 1
B = a - 1
C =(b-c+6) - (7-a+b) + c
C = b - c + 6 - 7 + a - b + c
C = a - 1
Chúc em học tốt!!!