Solve for x∈C x^3 +(4−3i)x^2 −(51+49i)x−442+170i=0


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Question Number 204999 by Frix last updated on 05/Mar/24

$Solve for x \in C$ $x^{3} + (4 - 3 i) x^{2} - (51 + 49 i) x - 442 + 170 i = 0$
	Answered by Skabetix last updated on 05/Mar/24

	$S = {- 9 - 4 i; - 3 + 5 i; 8 + 2 i} ?$
	Commented by Frix last updated on 05/Mar/24

	$Your method ?$
	Commented by TonyCWX08 last updated on 06/Mar/24

	$R e a l A n s w e r :$ $- 8.651 + 6.543 i$ $- 4.331 - 2.06 i$ $8.982 - 1.483 i$ $M e t h o d : W o l f r a m A l p h a$
	Commented by Frix last updated on 06/Mar/24

	$Wolfram Alpha is wrong . {It}^{'} s not$ $possible to use {Cardano}^{'} s Solution in this$ $case .$
	Commented by TonyCWX08 last updated on 08/Mar/24

	$A r e y o u s u r e ? ?$ $H o w y o u k n o w W o l f r a m A l p h a u d e {C a r d a n o}^{'} s F o r m u l a ? ?$
	Commented by Frix last updated on 08/Mar/24

	$Because your answer is wrong . Test your$ $solutions by inserting .$
	Answered by Rasheed.Sindhi last updated on 08/Mar/24

	$l e t x = a + b i$ $▸ {(a + b i)}^{3} + (4 - 3 i) {(a + b i)}^{2} - (51 + 49 i) (a + b i) - 442 + 170 i = 0$ $▸ a^{3} + 3 a^{2} b i - 3 {a b}^{2} - b^{3} i$ $+ (4 - 3 i) (a^{2} + 2 a b i - b^{2})$ $- (51 a - 49 b + 49 a i + 51 b i)$ $- 442 + 170 i = 0$ $▸ a^{3} + 3 a^{2} b i - 3 {a b}^{2} - b^{3} i$ $+ 4 a^{2} + 8 a b i - 4 b^{2} - 3 a^{2} i + 6 a b + 3 b^{2} i$ $- 51 a + 49 b - 49 a i - 51 b i$ $- 442 + 170 i = 0$ $▸ \underset{\overset{}{&}}{a^{3} - 3 {a b}^{2} + 4 a^{2} - 4 b^{2} + 6 a b - 51 a + 49 b - 442 = 0}$ $3 a^{2} b - b^{3} + 8 a b - 3 a^{2} + 3 b^{2} - 49 a - 51 b + 170 = 0$ $▸ - 15 {a b}^{2} - 20 b^{2} + 30 a b + 245 b + 5 a^{3} + 20 a^{2} - 255 a - 2210 = 0$ $- 13 b^{3} + 39 b^{2} + 39 a^{2} b + 104 a b - 663 b - 39 a^{2} - 637 a + 2210 = 0$
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