Given-that-k-2-3k-5-0-determine-the-value-of-k-4-6k-3-9k-2-7-

Question Number 198902 by necx122 last updated on 25/Oct/23

G i v e n t h a t k^{2} - 3 k + 5 = 0, d e t e r m i n e

t h e v a l u e o f k^{4} - 6 k^{3} + 9 k^{2} - 7

Answered by witcher3 last updated on 25/Oct/23

(k^{2} - 3 k + 5) (k^{2} - 3 k - 5) + 18 = k^{4} - {6 k}^{3} + {9 k}^{2} - 7

= 0 . (k^{2} - 3 k - 5) + 18 = 18

Commented by necx122 last updated on 25/Oct/23

Thank you so much sir

Commented by witcher3 last updated on 25/Oct/23

y^{'} re welcom

Answered by Rasheed.Sindhi last updated on 25/Oct/23

k^{2} - 3 k + 5 = 0; k^{4} - 6 k^{3} + 9 k^{2} - 7 = ?

\Rightarrow k^{2} = 3 k - 5

\Rightarrow k^{3} = 3 k^{2} - 5 k = 3 (3 k - 5) - 5 k = 4 k - 15

\Rightarrow k^{4} = 4 k^{2} - 15 k = 4 (3 k - 5) - 15 k = - 3 k - 20

k^{4} - 6 k^{3} + 9 k^{2} - 7

= (- 3 k - 20) - 6 (4 k - 15) + 9 (3 k - 5) - 7

= - 3 k - 20 - 24 k + 90 + 27 k - 45 - 7

= 70 - 52 = 18