Question 60

If a + b + c = 11, ab + bc + ca = 3 and abc = —135, then what is the value of $$a^3 + b^3 + c^3$$?

Solution

$$a^3 + b^3 + c^3$$

= $$(a + b + c)[(a + b + c)^2 - 3(ab + bc + ac)] + 3abc$$

= $$(11)[(11)^2 - 3(3)] + 3 \times (-135) $$

= $$(11)[112] - 405$$

= 1132 - 405 = 827

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