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if-a-and-b-are-real-numbers-determine-a-necessary-and-sufficient-condition-so-as-the-equation-x-2-a-b-x-a-b-to-have-three-real-distinct-roots-




Question Number 154980 by mathdanisur last updated on 23/Sep/21
if  a  and  b  are real numbers  determine a necessary and sufficient  condition so as the equation  x^2  + ((a(√b))/x) = a + b  to have three real distinct roots.
ifaandbarerealnumbersdetermineanecessaryandsufficientconditionsoastheequationx2+abx=a+btohavethreerealdistinctroots.
Answered by mr W last updated on 24/Sep/21
x≠0, b>0  x^3 −(a+b)x+a(√b)=0  for three distinct roots:  (((a(√b))^2 )/4)−(((a+b)^3 )/(27))<0  ⇒4(a+b)^3 −27a^2 b>0
x0,b>0x3(a+b)x+ab=0forthreedistinctroots:(ab)24(a+b)327<04(a+b)327a2b>0
Commented by mathdanisur last updated on 24/Sep/21
Thank you Ser, how did you get 4 and 27  please
ThankyouSer,howdidyouget4and27please
Commented by mathdanisur last updated on 24/Sep/21
Thank you Ser
ThankyouSer
Commented by mr W last updated on 24/Sep/21
i just applied the cardano′s formula  for cubic equation.
ijustappliedthecardanosformulaforcubicequation.

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