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SSH:(20152-12):10+1=2015
(12-22)+(32-42)+(52-62)+...+(20132-20142)+20152
-10+(-10)+(-10)+...+(-10)+20152
-10x(2015-1):2+20152=12
=> C=12
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\(102^2-2^2=\left(102-2\right)\left(102+2\right)=100.104=10400\)
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P = x + 2 - x - 8 2 = 10 2 = 100.
Biểu thức P có giá trị bằng 100 tại mọi giá trị của x.
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\(48^2-42^2+64-52^2\)
\(=\left(48^2-52^2\right)-\left(42^2-64\right)\)
\(=\left(48^2-52^2\right)-\left(42^2-8^2\right)\)
\(=\left(48-52\right)\left(48+52\right)-\left(42+8\right)\left(42-8\right)\)
\(=-4\cdot100-50\cdot34\)
\(=-8\cdot50-50\cdot34\)
\(=-50\cdot\left(8+34\right)\)
\(=-50\cdot42\)
\(=-2100\)
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a) \(=\left(127+73\right)^2=200^2=40000\)
b) \(=18^8-\left(18^8-1\right)=1\)
c) \(=\left(100+99\right)\left(100-99\right)+\left(98+97\right)\left(98-97\right)+...+\left(2+1\right)\left(2-1\right)\)
\(=100+99+98+97+...+2+1=5050\)
d) biến đổi thành \(20^2-19^2+18^2-17^2+..+2^2-1^2\)
rồi giải ra như trên
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\(72^2+144\cdot16+16^2-12^2\)
\(=\left(72^2+144\cdot16+16^2\right)-12^2\)
\(=\left(72^2+2\cdot72\cdot16+16^2\right)-12^2\)
\(=\left(72+16\right)^2-12^2\)
\(=88^2-12^2\)
\(=\left(88+12\right)\left(88-12\right)\)
\(=100\cdot76\)
\(=7600\)
= \(10^2+8^2+6^2+4^2+2^2-9^2-7^2-5^2-3^2-1\)-1
=\(55\)
\(\left(10^2+8^2+6^2+4^2+2^2\right)-\left(9^2+7^2+5^2+3^2+1^2\right)\)
\(=10^2+8^2+6^2+4^2+2^2-9^2-7^2-5^2-3^2-1^2\)
\(=\left(10^2-9^2\right)+\left(8^2-7^2\right)+...+\left(2^2-1^2\right)\)
\(=\left(10-9\right)\left(10+9\right)+\left(8-7\right)\left(8+7\right)+...+\left(2-1\right)\left(1+2\right)\)
\(=10+9+8+7+...+2+1\)
\(=\frac{\left(1+10\right)\cdot10}{2}\)
\(=55\)