If a + b + c = 15 and ab + bc + ca = 35, then find the value of a3 + b3 + c3- 3abc.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 1800.
Given that, a + b + c = 15 ...(i)
And ab + bc + ca = 35 ....(ii)
a3 + b3 + c3- 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca) ...(iii)
According to the given question,
Squarying both sides of equation (i),
⇒ (a + b + c)2 = 152
⇒ a2 + b2 + c2 + 2(ab + bc + ca) = 225
⇒ a2 + b2 + c2 + 2(35) = 225
⇒ a2 + b2 + c2 + 70 = 225
⇒ a2 + b2 + c2 = 155 ....(iv)
Putting the values of equation (i), (ii) and (iv) in equation (i),
⇒ a3 + b3 + c3- 3abc = (15)(155 - 35)
⇒ a3 + b3 + c3- 3abc = 15 × 120
⇒ a3 + b3 + c3- 3abc = 1800
Hence the required answer is 1800.