Question

If a2 + 1/a2 = 11, find the value of a3 - 1/a3​

Answer 1

Answer:

given a^2+1/a^2=11

(a+1/a)^2=13

(a+1/a)=sqrt13

(a-1/a)^2=(a+1/a)^2-4

=13-4=9

(a-1/a)=+or-3

we know that a^3-b^3=(a-b)(a^2+ab+b^2)

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

=3(12)

=36

Answer 2

Answer:

This is the simplified version of the answer given by @fayazmd4u above

Step-by-step explanation:

given $a^2+\frac{1}{a^2} =11$

$(a+\frac{1}{a^2})=13$

$(a+1/a)=13$

$(a-\frac{1}{a^2} )^2=(a+\frac{1}{a^2} )-4$

=13-4=9

$(a-1/a)=+or-3$

we know that $a^3-b^3=(a-b)(a^2+ab+b^2)$

$a^3-\frac{1}{a^3} = (a-\frac{1}{a} )(a^2+1+\frac{1}{a^2} )$

=$3 (12)$

$=36$