If a + b + c = 11 and ab + bc + ca = 15, then what is the value of $a^3 + b^3 + c^3 -3abc $ ?
Answer & explanation
Correct answer: option 2
Given,
a + b + c = 11
ab + bc + ca = 15
We know that,
a3 + b3 + c3 – 3abc = (a + b + c)[(a + b + c)2 – 3(ab + bc + ca)]
Calculation:
a3 + b3 + c3 - 3abc = [11{(11)2 - 3 × 15}]
= [11{121 – 3 × 15]
= [11{121 – 45}]
= 11 × 76
= 836