If a 4 - 1 a 4 119 what is the value of a 3 1 a 3

first of all question had ( a^4 + a^4 )= 119.
now coming to solution.
(a^2 + 1/a^2)^2 = a^4 + 1/a^4 +2
solving the above equation gives, (a^2 + 1/a^2) = 11
now writing , (a - 1/a)^2 = a^2 + 1/a^2 -2
solving this equation gives , (a-1/a)=3
now writing, (a - 1/a)^3 = ( a^3 - 1/a^3) - 3(a - 1/a)
so (a^3 - 1/a^3) = 27+9 = 36
solving the above equation gives , (a^3 - 1/a^3) = 36
cheers!!!!!!
11 years agoHelpfull: Yes(4) No(4)
If a^4 - 1/a^4 =119 what is the value of a^3 – 1/ a^3 ?
11 years agoHelpfull: Yes(3) No(3)
first of all question had ( a^4 + a^4 )= 119.
now coming to solution.
(a^2 + 1/a^2)^2 = a^4 + 1/a^4 +2
solving the above equation gives, (a^2 + 1/a^2) = 11 this is because A.M>=G.M(i.e you took +ve value 11)
now writing , (a - 1/a)^2 = a^2 + 1/a^2 -2 =11-2=9
solving this equation gives , (a-1/a)=3 or -3 because it does not satisfy A.M>=G.M hence we cannot determine expression a^3-(1/a)^3 because for a-1/a=3 we get a^3-(1/a)^3=36 and for a-1/a=-3 we get a3-(1/a)^3=-36 and it was not given in the question that a>0 or real number or whole num something like that
11 years agoHelpfull: Yes(3) No(1)
since a^4-1/a^4=119 so (a^2-1/a^2).(a^2+1/a^2)=1*119 or 7*17.but when we take the value as 7*17 it does not setisfied so (a^2-1/a^2)=1 nd (a^2+1/a^2)=119 so a+1/a=11.
now from a^2-1/a^2=1 so a-1/a=1/11.
since a^3-1/a^3=(a-1/a)(a^2+1/a^2+1)=120/11.
so ans will be 120/11.
11 years agoHelpfull: Yes(2) No(3)
was there any mention of x being > 0
11 years agoHelpfull: Yes(0) No(2)

If a^4 - 1/a^4 =119 what is the value of a^3 – 1/ a^3 ?