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solve-2x-99-3x-98-2x-97-3x-96-2x-3-0-in-R-




Question Number 91439 by Cynosure last updated on 30/Apr/20
solve 2x^(99) +3x^(98) +2x^(97) +3x^(96) +.....2x+3=0 in R
$${solve}\:\mathrm{2}{x}^{\mathrm{99}} +\mathrm{3}{x}^{\mathrm{98}} +\mathrm{2}{x}^{\mathrm{97}} +\mathrm{3}{x}^{\mathrm{96}} +…..\mathrm{2}{x}+\mathrm{3}=\mathrm{0}\:{in}\:\mathbb{R} \\ $$
Commented by Cynosure last updated on 30/Apr/20
pls i need answer
$${pls}\:{i}\:{need}\:{answer} \\ $$
Commented by Prithwish Sen 1 last updated on 30/Apr/20
The only real soln. for this equation is −(3/2)
$$\mathrm{The}\:\mathrm{only}\:\mathrm{real}\:\mathrm{soln}.\:\mathrm{for}\:\mathrm{this}\:\mathrm{equation}\:\mathrm{is}\:−\frac{\mathrm{3}}{\mathrm{2}} \\ $$
Answered by Rasheed.Sindhi last updated on 30/Apr/20
x^(98) (2x+3)+x^(96) (2x+3)+...+(2x+3)=0  (2x+3)(x^(98) +x^(96) +...+1)=0  • 2x+3=0⇒x=−3/2  •x^(98) +x^(96) +...+1=0  .......  ....
$${x}^{\mathrm{98}} \left(\mathrm{2}{x}+\mathrm{3}\right)+{x}^{\mathrm{96}} \left(\mathrm{2}{x}+\mathrm{3}\right)+…+\left(\mathrm{2}{x}+\mathrm{3}\right)=\mathrm{0} \\ $$$$\left(\mathrm{2}{x}+\mathrm{3}\right)\left({x}^{\mathrm{98}} +{x}^{\mathrm{96}} +…+\mathrm{1}\right)=\mathrm{0} \\ $$$$\bullet\:\mathrm{2}{x}+\mathrm{3}=\mathrm{0}\Rightarrow{x}=−\mathrm{3}/\mathrm{2} \\ $$$$\bullet{x}^{\mathrm{98}} +{x}^{\mathrm{96}} +…+\mathrm{1}=\mathrm{0} \\ $$$$……. \\ $$$$…. \\ $$
Commented by Cynosure last updated on 30/Apr/20
thanks
$${thanks} \\ $$

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