Given that k^2 −3k+5=0, determine the value of k^4 −6k^3 +9k^2 −7


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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

	$k^{2} - 3 k + 5 = 0; k^{4} - 6 k^{3} + 9 k^{2} - 7 = ?$ $\Rightarrow k^{2} = 3 k - 5$ $\Rightarrow k^{3} = 3 k^{2} - 5 k = 3 (3 k - 5) - 5 k = 4 k - 15$ $\Rightarrow k^{4} = 4 k^{2} - 15 k = 4 (3 k - 5) - 15 k = - 3 k - 20$ $k^{4} - 6 k^{3} + 9 k^{2} - 7$ $= (- 3 k - 20) - 6 (4 k - 15) + 9 (3 k - 5) - 7$ $= - 3 k - 20 - 24 k + 90 + 27 k - 45 - 7$ $= 70 - 52 = 18$
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