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
What will come in place of the question mark (?) in the following series?
168, 120, ?, 48, 24, 8
120, 126, 138, 162, ?, 306
In each of the following number series, one term is missing. Find the missing term.
121, 100, 81, ?, 49, 36
84, 105, ?, 168, 210, 259
480, 288, ?, 103.68, 62.208, 37.3248
42, 48, 60, 84, 132, ?
- 8, 12, 18, 27, ?
What will come in place of the question mark (?) in the following number series?
21, 42, 67, 96, ?, 166
11          20          ?             64          112        192
...14, 17, 23, 32, ?, 59
