A + 1/a= p find a^3 + 1/a^3

(1) p^3 + 3p

(2) 3p

(3) p^3 - 3p

​

9514 1404 393

  (3)  p^3 -3p

Step-by-step explanation:

  (a +1/a) = p . . . . . . . given

  (a +1/a)^3 = p^3 . . . . . . . . cube both sides

  a^3 +3a^2(1/a) +3a(1/a)^2 +(1/a)^3 = p^3 . . . . . . expand

  (a^3 +1/a^3) +3(a +1/a) = p^3 . . . . . . . . . . simplify, group

  (a^3 +1/a^3) +3p = p^3 . . . . . . . . . . substitute p for a+1/a

  (a^3 +1/a^3) = p^3 -3p . . . . . . subtract 3p from both sides

14

step-by-step explanation:

to find the perimeter, you add up all the lengths of the sides. in this case you would have to add up 18+22+40+80 which equals 160.