SOLUTION: If k^2=k+5, express the following in terms of k and a constant only. (i) k^3 (ii) k^4

Algebra ->  Real-numbers -> SOLUTION: If k^2=k+5, express the following in terms of k and a constant only. (i) k^3 (ii) k^4      Log On


   

Question 1176439: If k^2=k+5, express the following in terms of k and a constant only.
(i) k^3
(ii) k^4
Answer by ikleyn(52787) About Me  (Show Source):
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If k^2=k+5, express the following in terms of k and a constant only.
(a) k^3
(b) k^4
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(a)  k^3 = k*k^2 = replace k^2 by (k+5)  and continue

                 = k*(k+5) = k^2 + 5k = replace k^2 by (k+5) and continue 

                 = (k+5) + 5k = 6k + 5.     ANSWER



(b)  k^4 = k*k^3 = replace k^3 by (6k+5), based on (a), and continue

                 = k*(6k+5) = 6k^2 + 5k = replace k^2 ny (k+5)  and continue

                 = 6*(k+5) + 5k = 6k + 30 + 5k = 11k + 30.    ANSWER

Solved.