If x + y + z = 7, x2 + y2 + z2 = 85 and x3 + y3 + z3 = 913, then the value of is :
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e 4.
Here it is given that,
x + y + z = 7, x2 + y2 + z2 = 85 and x3 + y3 + z3 = 913.
One knows that,
(x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx)
⇒(7)2 = 85 + 2(xy + yz + zx)
xy + yz + zx = -18.............(1)
Now one also knows that,
x3 + y3 + z3 + 3xyz = (x + y + z)(x2 + y2 + z2 - (xy + yz + zx)
⇒ 913 + 3xyz = 7 × (85 + 18)
⇒ 913 + 3xyz = 721
⇒ xyz = 64
⇒ = 4.