Problem on Numbers

A set of numbers are put in the form of a puzzle. We need to analyze the given conditions and by assuming the unknown numbers equations are written to them. By those equations solve the unknown values. These usually involve around framing the complex statements about a single number. There is basic rule i.e. “start with ‘X'”.

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Some Basic Formulae:

1.    (a + b)(a - b) = (a² - b²)

2.    (a + b)² = (a² + b² + 2ab)

3.    (a - b)² = (a² + b² - 2ab)

4.    (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

5.    (a³ + b³) = (a + b)(a² - ab + b²)

6.    (a³ - b³) = (a - b)(a² + ab + b²)

7.    (a³ + b³ + c³ - 3abc) = (a + b + c)(a² + b² + c² - ab - bc – ac)