### Question 3

SSC-CGL 2020 Mar 4 Shift 2

If a + b + c = 7, ab + bc + ca = -6, then a³ + b³ + c³ - 3abc =?

### Solution in Detail

This is a formula based question. We know a³ + b³ + c³ - 3abc = (a+b+c) [(a + b + c)² - 3(ab + bc + ca)]. Substituting the given values we get = (7) (7² - 3(-6)) = 469 answer!

### Solution by Trick

Observe that there are 3 variables but 2 equations. If we set the third variable to any convenient value, the other two variables will adjust accordingly, and still the 2 given equations will remain satisfied! Let us take c = 0. So we have to find a³ + b³? We know that a³ + b³ = (a + b)³ - 3ab(a + b). Putting a + b = 7, and ab = -6, we get = 7³ - 3(7)(-6) = 469 ans!

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