Moi nguoi giup minh vs:
Rut gon bieu thuc:
a, 5^n +5^(n+2)
b,2/3. 3^(n-1)
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a: \(A=\left(2\sqrt{5}-3\sqrt{5}+3\sqrt{5}\right)\cdot\sqrt{5}=2\sqrt{5}\cdot\sqrt{5}=10\)
\(B=\dfrac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}-1}+\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}+1}\)
\(=\sqrt{x}-1+\sqrt{x}=2\sqrt{x}-1\)
b: A=2B
=>\(10=4\sqrt{x}-2\)
=>\(4\sqrt{x}=12\)
=>x=9(nhận)
\(3x^2-2x.\left(5+1,5x\right)+10\)
\(=3x^2-2x.5-2x.1,5x+10\)
\(=3x^2-3x^2-10x+10\)
\(=10-10x\)
\(=10.\left(1-x\right)\)
\(\frac{2x+2}{\left(x+1\right)\left(x-1\right)}.ĐKXĐ:x\ne\pm1\)
\(=\frac{2\left(x+1\right)}{\left(x+1\right)\left(x-1\right)}=\frac{2}{x-1}\)
~~
2A = 2 + 1 + 1/2 + 1/2^2 + ... + 1/2^2011
A = 1 + 1/2 + .. + 1/2^2011 + 1/2^2012
2A - A = 2 + 1 + 1/2 + .. + 1/2^2011 - 1 - 1/2 - ... - 1/2^2011 - 1/2^2012
A = 2 - 1/2^2012
A = \(\frac{2^{2012}-2}{2^{2012}}\)
A = 1+1/2+1/2^2+1/2^3+.....+1/2^2012
2A= 2. (1+1/2+1/2^2+1/2^3+.....+1/2^2012)
2A= 2 + 1 + 1/2 + 1/2^2 + 1/2^3 + ...+ 1/2^2011
2A - A= (2 + 1 + 1/2 + 1/2^2 + 1/2^3+ ...+ 1/2^2011) - (1+1/2+1/2^2+1/2^3+.....+1/2^2012)
1A= 2 + 1 + 1/2 + 1/2^2 + 1/2^3 + ...+ 1/2^2011 - 1-1/2-1/2^2+1/2^3+.....+1/2^2012
1A= 2 - 1/2^2012
A= 2-1/2^2012
A= 2 - 1/2^2012
Bài 2:
a: ĐKXĐ: \(x\notin\left\{0;2;-2;3\right\}\)\(A=\left(\dfrac{-\left(x+2\right)}{x-2}-\dfrac{4x^2}{\left(x-2\right)\left(x+2\right)}+\dfrac{x-2}{x+2}\right):\dfrac{x\left(x-3\right)}{x^2\left(2-x\right)}\)
\(=\dfrac{-x^2-4x-4-4x^2+x^2-4x+4}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{-x\left(x-2\right)}{x-3}\)
\(=\dfrac{-4x^2-8x}{\left(x+2\right)}\cdot\dfrac{-x}{x-3}\)
\(=\dfrac{-4x\left(x+2\right)}{x+2}\cdot\dfrac{-x}{x-3}=\dfrac{4x^2}{x-3}\)
b: Để A>0 thì x-3>0
hay x>3
a, 5^n +5^(n+2)
=5(5n-1+5n+1)
=26*5n
b,2/3. 3^(n-1)
=2*3n-2