Latest Elitmus Aptitude Question SOLUTION: if a power 4 +(1/a)power 4=119 then a power 3-(1/a)power 3= a)32 b)39 c)data not sufficient

Since a power 4 +1/a poeer 4 = 119

step 1. Re write the question as-
=> (a square) power 2 + 1/(a square 2) power 2 = 119

step 2 - add 2 and substract 2 on left side
=> (a square) power 2 + 1/(a square 2) power 2 + 2 -2= 119

step 3- apply (A+B)s quare = A square + B square + 2 *A *B
=> (a square) power 2 + 1/(a square 2) power 2 + 2((a square) power 2) * (1/(a square 2) power 2) - 2((a square) power 2) * (1/(a square 2) power 2)= 119
=> ((a square ) + 1/ (a square) ) )square = 119 + 2 = 121
=> (a square ) + 1/ (a square) ) = square root of (121)
=>(a square ) + 1/ (a square) ) = 11 .....................................En(1)

step 4- substract 2 and add 2 on left side
=>(a square ) + 1/ (a square) ) - 2 + 2 = 11
=> (a square ) + 1/ (a square) ) - 2 * (a square ) + 1/ (a square) + 2 (a square ) + 1/ (a square) = 11
=> (a - 1/a) square = 11-2 = 9
=> a - 1/a = square root of 9
=> a - 1/a = 3.....................................En(2)

NOW problem is-
=a power 3 - 1/a power 3
= (a - 1/a) * (a sqaure + (a square) * (1/a square) + 1/a square)
= 3 * (a sqaure + 1/a square + 1) [ FROM EQN(2) ]
= 3 * ( 11 + 1) [ FROM EQN(1) ]
= 3 * 12
=36 ANS

sorry correct formula is
x^3-1/x^3=(x-1/x)(x^2+x.1/x+1/x^2)
3.(11+1)
36 is correct ans

Ans =36
and options is 32
36
39
can not determine

a power4 +(1/a)power4=119
((a power4)square+1) / a power 4=119
now apply the formula of (a square+b square)=(a+b)sauare-2ab;

(a power4 + 1) square -2*a power4=119* a power4
(apower4+1)square =121 *apower4
(apower4+1)= square root(121*apower4)
or (apower4+1) =11*a square;
apower4-11a square +1=0 now we have a equation solve this and get a value of 'a'


final answer should be approx 81

x^4+1/x^4=119
let x2=y
y^2+1/y^2=119
(y+1/y)^2-2.y.1/y=119
(y+1/y)^2=121
y+1/y=11 eq 1
x^2+1/x^2=11
(x-1/x)^2+2.x.1/x=11
(x-1/x)^2=9
x-1/x=3 eq 2
x^3-1/x^3=(x-1/x)(x^2-x.1/x+1/x^2)
3.(11-1)
30 is ans

use a3-b3= (a-b) (a2+ab+b2)
a4-b4=(a2+b2)2

a^4+1/a^4=119,(a2)^2++1/(a2)^2+2*a2*1/a^2-2*a^2*1/a2
(a2+1/a2)^2-2=119 a2+1/a2=11
a3-1/a3=(a-1/a)(a2+1/a2+2)
a-1/a=3
13*3=39