### Question 5

SSC-CGL 2020 Mar 4 Shift 1

If a + b + c = 11, ab + bc + ca = 3 and abc = -135, then a³ + b³ + c³ =?

### Solution in Short

Start with abc = -135. Factorize 135 as 3 x 5 x 9. What combination gives 11? 9 + 5 + (-3). So take a = 9, b = 5, c = -3 and we can verify that ab + bc + ca is equal to 3. Hence a³ + b³ + c³ = 9³ + 5³ + (-3)³ = 827 answer!

### Solution in Detail

This is a formula based question. We know this standard algebraic identity a³ + b³ + c³ = (a+b+c) [(a+b+c)² - 3(ab + bc + ca)] + 3abc. Substituting the given values we get a³ + b³ + c³ = 11 x [11² - 3 x (3)] + 3 x (-135) = 827 answer!

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