Question

(a+1/a)^2=3,then a^3+1/a^3=

Answer 1

Answer:

Step-by-step explanation:

(a+1a)2=3(a+1a)2=3 ---> (a+1a)=30.5(a+1a)=30.5 ...(1)

Now, (a3+1a3)(a3+1a3) = (a+1a)3−3∗(a+1a)(a+1a)3−3∗(a+1a) ....[ as (a+b)3=a3+b3+3ab(a+b)(a+b)3=a3+b3+3ab(a+b)]

Thus, (a3+1a3)(a3+1a3) = (a+1a)3−3∗(a+1a)(a+1a)3−3∗(a+1a) = 31.5−3∗30.531.5−3∗30.5 = 0.