Latest self Aptitude Question SOLUTION: if a+(1)/a=1, then the value of a^3 is

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if a+(1)/a=1, then the value of a^3 is

Arjun (11 years ago)

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A R APURVA   (11 years ago)

a+(1)/a=1,we can write
(a+(1)/a)^3=1^3
a^3+(1/a)^3+3=1
a^3+(1/a)^3=-2
a=-1

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kck  (11 years ago)

Answer: 0.
Explanation:
a+1/a=1;
a^2 +1 = a or a^2 - a +1 =0;
now a^3=(1-1/a)^3=(1-1/a)(1 -1/a+1/a^2)=(1-1/a)((a^2 - a +1)/a) =0;

Is this solution Helpfull? Yes (3) | No (7)  

PARAG KAMRA  (11 years ago)

if a+(1)/a=1,then
a=1-1/a

a^3=(1-1/a)^3
so we can see (1-1/a)^3 as (a-b)^3
(a-b)^3=a^3-b^3-3ab(a-b)
a^3-b^3-3a^2b+3ab^2
likeas

(1-1/a)^3=(1)^3-(1/a)^3-3/a+3/a^2
=1-1/a^3-3/a+3/a^2
=(1-3/a)+(3/a^2-1/a^3)
=1/a((1/a)-3)-1/a^2((1/a)-3)
=((1/a)-3)(1/a-1/a^2)
so from this we can find roots
(1/a)-3=0
3a-1=0 a=1/3

(1/a)-(1/a^2)=0
(a-1)/a^2=0
a=1
so value of a is 1, 1/3
so value of a^3 can be 1,1/9(ans)

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Anurag  (11 years ago)

a+1/a=1
a^2-a+1=0
solving,a=-(4+i(3)^0.5)/4 and .....

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