Question
If x + y + z = 4, xyz = 6 & x2 +
y2 + z2 = 8 then find the value of x3 + y3 + z3.Solution
We know the identity (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc (4)2 = 8 + 2(xy + yz + zx) (xy + yz + zx) = 8/2 = 4 a3 + b3 + c3 = (a + b + c) (a2 + b2 + c2 – ab – bc – ca) + 3abc So, x3 + y3 + z3 = 4(8 – (4)) + 3(6) = 16 + 18 = 34
More Algebra Questions
What will come in place of (?) question mark in the given number series.
16, 24, 51, 115, 240, ?
Find the missing number in the given number series.
512, 128, 32, 8, ?, 171, 79, 88, 152, ?, 393
15, 31, 67, 131, ?, 375
1, 26, 75, 156, 277, ?
7 29 61 ? 211 349
...18   29   16   31   ?   33
72, 82, 62, 102, 22, ?
?, 15, 45, 225, 1575, 14175
166    156    136   ?     66    16
