Question

if (a+1/a)^2=b then a^3+1/a^3=?

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Answer 1

Answer:

Step-by-step explanation:

a^3 +b^3 = a^2 - ab + b^2

(a^3+ 1/a^3) = ( a+ 1/a) ( a^2 -1 +1/a^2) (1) equation

it is given that

(a+1/a)^2 = 3

or

( a+ 1/a) = √3. (2) equation

Also

( a+ 1/a)^2 = 3

or - a^2 + 1/a^2 +2 =3

then ( transpose 2 to subtract 3)

a^2 + 1/a^2 = 3-2

a^2 + 1/a^2 = 1. (3) equation

putting 2 and 3 in 1 we have

a^3 +1/a^3 = √3 (1-1) = 0