if a^2-5a-1=0, evaluate (1) a^2+1/a^2, (2) a^3-1/a^3
Answers
Answered by
5
=> a^2 - 5a - 1 = 0
=> a^2 - 1 = 5a
=> (a^2 - 1)/a = 5a/a {divide by a}
=> a - 1/a = 5 ...(1)
(i) Square on both sides of (1),
=> (a - 1/a)^2 = 5^2
=> a^2 + 1/a^2 - 2 = 25
=> a^2 + 1/a^2 = 27
(ii) Cube on both sides of (1),
=> (a - 1/a)^3 = 5^3
=> a^3 - 1/a^3 - 3(a * 1/a)(a - 1/a) = 125
=> a^3 - 1/a^3 - 3(1)(5) = 125 {a - 1/a = 5}
=> a^3 - 1/a^3 = 125 + 15 = 140
Similar questions