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12: \(3\left(2^2+1\right)\left(2^4+1\right)\cdot\ldots\cdot\left(2^{64}+1\right)+1\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\cdot\ldots\cdot\left(2^{64}+1\right)+1\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\cdot\ldots\cdot\left(2^{64}+1\right)+1\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\cdot\left(2^{32}+1\right)\cdot\left(2^{64}+1\right)+1\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\cdot\left(2^{32}+1\right)\cdot\left(2^{64}+1\right)+1\)
\(=\left(2^{32}-1\right)\cdot\left(2^{32}+1\right)\cdot\left(2^{64}+1\right)+1\)
\(=\left(2^{64}-1\right)\cdot\left(2^{64}+1\right)+1\)
\(=2^{128}-1+1=2^{128}\)
11: \(100^2-99^2+98^2-97^2+\cdots+2^2-1^2\)
=(100-99)(100+99)+(98-97)(98+97)+...+(2-1)(2+1)
=100+99+...+2+1
\(=\frac{100\left(100+1\right)}{2}=5050\)
10: \(\left(a+b+c\right)^2+\left(a+b-c\right)^2-2\left(a+b\right)^2\)
\(=\left(a+b\right)^2+2c\left(a+b\right)+c^2+\left(a+b\right)^2-2c\left(a+b\right)+c^2-2\left(a+b\right)^2\)
\(=2c^2\)
9: \(\left(x+1\right)^3+\left(x-1\right)^3+x^3-3x\left(x+1\right)\left(x-1\right)\)
\(=x^3+3x^2+3x+1+x^3-3x^2+3x-1+x^3-3x\left(x^2-1\right)\)
\(=3x^3+6x-3x^3+3x=9x\)
7: \(\left(6x+1\right)^2+\left(6x-1\right)^2-2\left(6x+1\right)\left(6x-1\right)\)
\(=\left(6x+1\right)^2-2\left(6x+1\right)\left(6x-1\right)+\left(6x-1\right)^2\)
\(=\left(6x+1-6x+1\right)^2=2^2=4\)
6: \(\left(2x+1\right)^2+\left(3x-1\right)^2+2\left(2x+1\right)\left(3x-1\right)\)
\(=\left(2x+1+3x-1\right)^2=\left(5x\right)^2=25x^2\)
5: \(\left(4x-5\right)\left(2x+3\right)-4\left(x+2\right)\left(2x-1\right)+10x+7\)
\(=8x^2+12x-10x-15-4\left(2x^2-x+4x-2\right)+10x+7\)
\(=8x^2+2x-15-8x^2-12x+8+10x+7\)
=-15+8+7
=0
4: (x+2)(x-2)-(x-3)(x+1)
\(=x^2-4-\left(x^2+x-3x-3\right)\)
\(=x^2-4-x^2-x+3x+3\)
=2x-1
3: \(3x\left(x-2\right)-5x\left(1-x\right)-8\left(x^2-3\right)\)
\(=3x^2-6x-5x+5x^2-8x^2+24\)
=-11x+24
2: \(3\left(2x-1\right)-5\left(x-3\right)+6\left(3x-4\right)-19x\)
=6x-3-5x+15+18x-24-19x
=(6x-5x+18x-19x)+(-3+15-24)
=0+12-24
=12-24
=-12
1: \(x\left(3x+12\right)-\left(7x-20\right)+x^2\left(2x-3\right)-x\left(2x^2+5\right)\)
\(=3x^2+12x-7x+20+2x^3-3x^2-2x^3-5x\)
=20
1029-896:34x21
=1029-448/17 x 21
=1029-9408/17
=8085/17
Vì phân số càn tìm bé hơn 1 nên tử của phân số đó bé hơn mẫu
Tử của phân số là:
(30-4):2=13
Mẫu của phân số là:
30-13=17
Vậy phân số cần tìm là:\(\dfrac{13}{17}\)
\(\dfrac{13}{17}\)