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Question Number 169653 by infinityaction last updated on 05/May/22
     solve for x        x^2  + (x^2 /((x+1)^2 ))   =  3
$$ \\ $$$$\:\:\:{solve}\:{for}\:{x} \\ $$$$\:\:\:\:\:\:{x}^{\mathrm{2}} \:+\:\frac{{x}^{\mathrm{2}} }{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }\:\:\:=\:\:\mathrm{3} \\ $$
Answered by mr W last updated on 05/May/22
x^2 −(3−x^2 )(x+1)^2 =0  x^4 +2x^3 −x^2 −6x−3=0  (x^2 −x−1)(x^2 +3x+3)=0  x^2 −x−1=0  ⇒x=((1±(√5))/2)  x^2 +3x+3=0  ⇒x=((−3±i(√3))/2)
$${x}^{\mathrm{2}} −\left(\mathrm{3}−{x}^{\mathrm{2}} \right)\left({x}+\mathrm{1}\right)^{\mathrm{2}} =\mathrm{0} \\ $$$${x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} −\mathrm{6}{x}−\mathrm{3}=\mathrm{0} \\ $$$$\left({x}^{\mathrm{2}} −{x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{3}\right)=\mathrm{0} \\ $$$${x}^{\mathrm{2}} −{x}−\mathrm{1}=\mathrm{0} \\ $$$$\Rightarrow{x}=\frac{\mathrm{1}\pm\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{3}=\mathrm{0} \\ $$$$\Rightarrow{x}=\frac{−\mathrm{3}\pm{i}\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$
Commented by infinityaction last updated on 05/May/22
thank you sir
$${thank}\:{you}\:{sir} \\ $$

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