| a | -(-1) |
| -a | ......... |
| |a| | ......... |
| a^2 | ......... |
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| a | -(-1) |
| -a | -1 |
| IaI | 1 |
| a^2 | 1 |
e: \(\left(a^2-1\right)\left(a^2+a+1\right)\left(a^2-a+1\right)\)
\(=\left(a^3-1\right)\left(a^3+1\right)\)
\(=a^6-1\)
a: \(A=\left(1-\dfrac{2\sqrt{a}}{a+1}\right):\dfrac{1}{\sqrt{a}+1}-\dfrac{2\sqrt{a}}{\left(a+1\right)\left(\sqrt{a}+1\right)}\)
\(=\dfrac{\left(\sqrt{a}-1\right)^2}{a+1}\cdot\dfrac{\sqrt{a}+1}{1}-\dfrac{2\sqrt{a}}{\left(a+1\right)\left(\sqrt{a}+1\right)}\)
\(=\dfrac{\left(a-1\right)^2-2\sqrt{a}}{\left(a+1\right)\left(\sqrt{a}+1\right)}=\dfrac{a^2-2a+1-2\sqrt{a}}{\left(a+1\right)\left(\sqrt{a}+1\right)}\)
b: Khi \(a=2000-2\sqrt{1999}\) thì \(A=\dfrac{\left(1999-2\sqrt{1999}\right)^2-2\left(\sqrt{1999}-1\right)}{\left(2001-2\sqrt{1999}\right)\left(\sqrt{1999}-1+1\right)}\)
\(\simeq42,66\)
a, đề phải là 1/a.(a+1) = 1/a - 1/a+1 chứ bạn !
Có : 1/a.(a+1) = (a+1)-a/a.(a+1) = a+1/a.(a+1) - a/a.(a+1) = 1/a - 1/a+1
=> 1/a.(a+1) = 1/a - 1/a+1
b, Có : 2/a.(a+1).(a+2) = (a+2)-a/a.(a+1).(a+2) = a+2/a.(a+1).(a+2) - a/a.(a+1).(a+2) = 1/a.(a+1) - 1/(a+1).(a+2)
=> 2/a.(a+1).(a+2) = 1/a.(a+1) - 1/(a+1).(a+2)
Tk mk nha
a, \(VP=\frac{1}{a}-\frac{1}{a+1}=\frac{a+1}{a\left(a+1\right)}-\frac{a}{a\left(a+1\right)}==\frac{a+1-a}{a\left(a+1\right)}=\frac{1}{a\left(a+1\right)}=VT\)
b, \(VP=\frac{1}{a\left(a+1\right)}-\frac{1}{\left(a+1\right)\left(a+2\right)}=\frac{a+2}{a\left(a+1\right)\left(a+2\right)}-\frac{a}{a\left(a+1\right)\left(a+2\right)}=\frac{a+2-a}{a\left(a+1\right)\left(a+2\right)}=\frac{2}{a\left(a+1\right)\left(a+2\right)}=VT\)
ĐKXĐ: a<>1; a<>0; a<>-1
a: \(P=\dfrac{a\left(a+1\right)}{\left(a-1\right)^2}:\dfrac{a^2-1+a+2-a^2}{a\left(a-1\right)}\)
\(=\dfrac{a\left(a+1\right)}{\left(a-1\right)^2}\cdot\dfrac{a\left(a-1\right)}{a+1}=\dfrac{a^2}{a-1}\)
b: Khi P=-1/2 thì a^2/(a-1)=-1/2
=>2a^2=-a+1
=>2a^2+a-1=0
=>2a^2+2a-a-1=0
=>(a+1)(2a-1)=0
=>a=1/2(nhận) hoặc a=-1(loại)
c: \(P=\dfrac{a^2-1+1}{a-1}=a+1+\dfrac{1}{a-1}=a-1+\dfrac{1}{a-1}+2\)
=>\(P>=2\cdot\sqrt{\left(a-1\right)\cdot\dfrac{1}{a-1}}+2=4\)
Dấu = xảy ra khi a-1=1
=>a=2