if x + 1/x = 4 then 6[x^2 + 1/x^2] + 9[x^3 + 1/x^3] will be

M4maths Previous Puzzles

29 Feb 2012 x + 1/x

if x + 1/x = 4
then 6[x^2 + 1/x^2] + 9[x^3 + 1/x^3] will be

OPtion

1) 448
2) 502
3) 552
4) 602
5) 608
6) 660
7) 668
8) 694
9) 682
10) none of these

Solution

x^2 + 1/x^2 = [x + 1/x]^2 - 2
x^3 + 1/x^3 = [x + 1/x]^3 - 3[x + 1/x]
on applying values we can obtain the correct answer 552

Correct Option: 3 Best Solution (4)

Tijo Jose   12 years AGO

x + 1/x = 4
(x + 1/x)^2 = x^2 + 2*x*(1/x) + 1/x^2 = x^2 + 1/x^2 + 2
So, x^2 + 1/x^2 = (x + 1/x)^2 -2 = 4^2 - 2 = 14
Similarly, (x + 1/x)^3 = x^3 + 1/x^3 + 12
So, x^3 + 1/x^3 = (x + 1/x)^3 - 12 = 64 - 12 = 52
Therefore,
6[x^2 + 1/x^2] + 9[x^3 + 1/x^3]
= (6 * 14) + (9 * 52)
= 552

Like? Yes (4) | No (3)  

Maneesh Chaubey   12 years AGO

x+1/x=4
squaring the above term we get,
x^2 + 1/x^2=14
14*6=84
(x+1/x=4)^3=52 the above term we get,
52*9=468
then 468+84=552
hence option 3 is correct.

Like? Yes (2) | No (3)  

MAYANK NIGAM   12 years AGO

6*14+52*9=552

Like? Yes (1) | No (4)  

pathan   12 years AGO

by using following:
a^2+b^2=(a+b)^2-2ab
a^3+b^3=(a + b)(a^2+b^2-ab)

Like? Yes (1) | No (4)