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If a−b=4a-b=4a−b=4 and ab=45ab=45ab=45, what is the value of a3−b3a^3 -b^3a3−b3?
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Given that aaa, bbb and ccc are real numbers such that abc=1abc=1abc=1, find the value of (aab+a+1+bbc+b+1+cca+c+1)2.\left(\frac{a}{ab+a+1}+\frac{b}{bc+b+1}+\frac{c}{ca+c+1}\right)^2.(ab+a+1a+bc+b+1b+ca+c+1c)2.
1+3+5+7+…+1992+4+6+8+…+200= ? \large \frac{1 + 3 + 5 + 7 +\ldots+ 199}{2 + 4 + 6 + 8 +\ldots+ 200} = \ ? 2+4+6+8+…+2001+3+5+7+…+199= ?
12+22+32+⋯+20122+20132+201421+2+3+⋯+2012+2013+2014= ?\large \frac{1^2+2^2+3^2+\cdots+2012^2+2013^2+2014^2}{1+2+3+\cdots+2012+2013+2014} = \ ? 1+2+3+⋯+2012+2013+201412+22+32+⋯+20122+20132+20142= ?
Hint: 12+22+32+⋯+n2=16n(n+1)(2n+1) 1^2 + 2^2 + 3^2 + \cdots + n^2= \frac16 n(n+1)(2n+1) 12+22+32+⋯+n2=61n(n+1)(2n+1).
{x2−y2=4−2xyx+y=2 \large { \begin{cases} {x^2-y^2=4-2xy} \\ { x+ y = 2 } \end{cases} } ⎩⎨⎧x2−y2=4−2xyx+y=2
If xxx and yyy satisfy the system of equations above, find the value of x−yx-yx−y.
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