zúp mik câu 4, 5, 6 với ạ
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\(=\dfrac{2-1}{1x2}+\dfrac{3-2}{2x3}+\dfrac{4-3}{3x4}+...+\dfrac{10-9}{9x10}=\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}=\)
\(=1-\dfrac{1}{10}=\dfrac{9}{10}\)
Ta có : \(\frac{x-2}{5}=\frac{3-y}{7}=\frac{\left(x-2\right)-\left(3-y\right)}{5-7}=\frac{x-2-3+y}{-2}\) \(=\frac{x+y-5}{-2}=\frac{-2}{-2}=1\)
Nên : \(\frac{x-2}{5}=1\Rightarrow x-2=5\Rightarrow x=7\)
\(\frac{3-y}{7}=1\Rightarrow3-y=7\Rightarrow y=-4\)
Vậy x = 7 ; y = -4
\(\frac{x-2}{5}=\frac{3-y}{7}\)
Áp dụng tính chất dãy tỉ số bằng nhau , ta có :
\(\frac{x-2}{5}=\frac{3-y}{7}=\frac{x-2-3+y}{5-7}=\frac{3-2-3}{5-7}=\frac{-2}{-2}=1\)
\(\Rightarrow\hept{\begin{cases}x-2=5\\3-y=7\end{cases}}\Rightarrow\hept{\begin{cases}x=7\\y=-4\end{cases}}\)
4: Ta có: \(x^2+10x+25=0\)
\(\Leftrightarrow x+5=0\)
hay x=-5
5: Ta có: \(x^2-x+\dfrac{1}{4}=0\)
\(\Leftrightarrow x-\dfrac{1}{2}=0\)
hay \(x=\dfrac{1}{2}\)
6: Ta có: \(x^2-10x+25=0\)
nên x-5=0
hay x=5
Câu 2:
1:
a: a>b
nên -2a<-2b
=>-2a+1<-2b+1
b: a>b
nên 5a>5b
=>5a+1>5b+1>5b-1
2: \(A=x^2+2x+1+4=\left(x+1\right)^2+4>=4\)
Dấu '=' xảy ra khi x=-1
Câu 3:
1) \(\left|x+7\right|=1-2x\) (*)
-ĐK: \(1-2x\ge0\Leftrightarrow-2x\ge-1\Leftrightarrow x\le\dfrac{1}{2}\)
(*) \(\Leftrightarrow x+7=1-2x\) hay \(x+7=2x-1\)
\(\Leftrightarrow x+2x=1-7\) hay \(x-2x=-1-7\)
\(\Leftrightarrow3x=-6\) hay \(-x=-8\)
\(\Leftrightarrow x=-2\) (nhận) hay \(x=8\) (loại)
-Vậy \(S=\left\{-2\right\}\)
\(4,=\left(a-3-2\right)\left(a-3+2\right)=\left(a-5\right)\left(a-1\right)\\ 5,=\left(a-2b+b\right)\left(a-2b-b\right)=\left(a-b\right)\left(a-3b\right)\\ 6,=\left(4a-3b\right)\left(16a^2+12ab+9b^2\right)\)
1. a2 - 4b2
= a2 - (2b)2
= (a - 2b)(a + 2b)
2. 16a2 - b4
= (4a)2 - (b2)2
= (4a - b2)(4a + b2)
3. 4a4 - 81b4
= (2a2)2 - (9b2)2
= (2a2 - 9b2)(2a2 + 9b2)
4. (a - 3)2 - 4
= (a - 3)2 - 22
= (a - 3 - 2)(a - 3 + 2)
= (a - 5)(a - 1)
5. (a - 2b)2 - b2
= (a - 2b - b)(a - 2b + b)
= (a - 3b)(a - b)
6. 64a3 - 27b3
= (4a)3 - (3b)3
= (4a - 3b)(16a2 + 12ab + 9b2)
\(a,=\dfrac{20}{60}+\dfrac{12}{60}-\dfrac{15}{60}\\ =\dfrac{17}{60}\\ b,=\dfrac{7}{8}-\left(\dfrac{5}{20}+\dfrac{8}{20}\right)\\ =\dfrac{7}{8}-\dfrac{13}{20}\\ =\dfrac{35}{40}-\dfrac{26}{40}=\dfrac{9}{40}\\ c,=\dfrac{5}{11}-\dfrac{3}{55}=\dfrac{25}{55}-\dfrac{3}{55}=\dfrac{22}{55}=\dfrac{2}{5}\)
a: =20/60+12/60-15/60=17/60
b: =7/8-1/4-2/5=5/8-2/5=25/40-16/40=9/40
c: =5/11-3/5+6/11=1-3/5=2/5