Rút gọn:
a. ababab/cdcdcd b. aaaa/bbbb
[c>0,b>0]
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a) a b = a . ( − 1 ) b . ( − 1 ) = − a − b
b) ta có:
a b a b ¯ c d c d ¯ = a b a b ¯ : 101 c d c d ¯ : 101 = a b ¯ c d ¯ ; a b a b a b ¯ c d c d ¯ c d = a b a b a b ¯ : 10101 c d c d ¯ c d:10101 = a b ¯ c d ¯
do đó: a b a b ¯ c d c d ¯ = a b a b a b ¯ c d c d ¯ c d
c) a b a b ¯ a b a b a b ¯ = a b a b ¯ : a b ¯ a b a b a b ¯ : a b ¯ = 101 10101
`a)sqrt{(sqrt7-4)^2}+sqrt7`
`=|sqrt7-4|+sqrt7`
`=4-sqrt7+sqrt7=4`
`b)\sqrt{81a}-sqrt{144a}+sqrt{36a}(a>=0)`
`=9sqrta-12sqrta+6sqrta=3sqrta`
a) Ta có: \(\sqrt{\left(\sqrt{7}-4\right)^2}+\sqrt{7}\)
\(=4-\sqrt{7}+\sqrt{7}\)
=4
b) Ta có: \(\sqrt{81a}-\sqrt{144a}+\sqrt{36a}\)
\(=9\sqrt{a}-12\sqrt{a}+6\sqrt{a}\)
\(=3\sqrt{a}\)
\(\frac{52}{75}=\frac{52.101}{75.101}=\frac{5252}{7575};\frac{52}{75}=\frac{52.10101}{75.10101}=\frac{525252}{757575}\)
\(\frac{13}{15}=\frac{13.101}{15.101}=\frac{1313}{1515};\frac{13}{15}=\frac{13.10101}{15.10101}=\frac{131313}{151515}\)
\(\frac{ab}{cd}=\frac{101ab}{101cd}=\frac{abab}{cdcd};\frac{ab}{cd}=\frac{10101ab}{10101cd}=\frac{ababab}{cdcdcd}\)
ai k minh minh k lai
Ta co :
\(\frac{abab}{cdcd}\) va \(\frac{ababab}{cdcdcd}\)
\(\Rightarrow\frac{abab}{cdcd}=\frac{ab}{cd}\)
\(\Rightarrow\frac{ababab}{cdcdcd}=\frac{ab}{cd}\)
Ta thay :\(\frac{ab}{cd}=\frac{ab}{cd}\)
Vay :\(\frac{abab}{cdcd}=\frac{ababab}{cdcdcd}\)
cấm ai đc copy bài tớ
aaaaxb=bbbbxa .......vì phép nhân có tính chất giao hoán
\(A=x-4-\sqrt{x^4-8x^2+16}=x-4-\sqrt{[\left(x-2\right)\left(x+2\right)]^2}\)
\(A=x-4-\left(x-2\right)\left(x+2\right)=x-4-\left(x^2-4\right)=-x^2+x\)
\(B=\dfrac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\sqrt{a}-\sqrt{b}}.\left(\sqrt{a}+\sqrt{b}\right)=a-b\)
a b a b ¯ c d c d ¯ = a b ¯ c d ¯ . 101 101 = a b ¯ c d ¯
a b a b a b ¯ c d c d c d ¯ = a b ¯ c d ¯ . 10101 10101 = a b ¯ c d ¯
⇒ a b a b ¯ c d c d ¯ = a b a b a b ¯ c d c d c d ¯
a b a b ¯ c d c d ¯ = 101 a b ¯ 101 c d ¯ = a b ¯ c d ¯ ; a b a b a b ¯ c d c d c d ¯ = 10101 a b ¯ 10101 c d ¯ = a b ¯ c d ¯
⇒ a b a b ¯ c d c d ¯ = a b a b a b ¯ c d c d c d ¯
\(a.\frac{ababab}{cdcdcd}\)
\(=\frac{10000ab+100ab+ab}{10000cd+100cd+cd}\)
\(=\frac{ab\left(10000+100+1\right)}{cd\left(10000+100+1\right)}\)
\(=\frac{ab}{cd}\)
\(b.\frac{aaaa}{bbbb}\)
\(=\frac{1000a+100a+10a+a}{1000b+100b+10b+b}\)
\(=\frac{a\left(1000+100+10+1\right)}{b\left(1000+100+10+1\right)}\)
\(=\frac{a}{b}\)