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x-1-3x-2-2-3x-2-x-1-3-Find-the-value-of-x-




Question Number 5765 by sanusihammed last updated on 26/May/16
(√((x−1)/(3x+2)))   +  2 ((√((3x+2)/(x−1))) )  =  3    Find the value of x
$$\sqrt{\frac{{x}−\mathrm{1}}{\mathrm{3}{x}+\mathrm{2}}}\:\:\:+\:\:\mathrm{2}\:\left(\sqrt{\frac{\mathrm{3}{x}+\mathrm{2}}{{x}−\mathrm{1}}}\:\right)\:\:=\:\:\mathrm{3} \\ $$$$ \\ $$$${Find}\:{the}\:{value}\:{of}\:{x}\: \\ $$
Commented by prakash jain last updated on 27/May/16
(√((x−1)/(3x+2)))=u  u+(2/u)=3  u^2 −3u+2=0  (u−2)(u−1)=0⇒u=2 or u=1  u=2⇒((x−1)/(3x+2))=4⇒x−1=12x+8⇒x=−(9/(11))  u=1⇒((x−1)/(3x+1))=1⇒x−1=3x+1⇒x=−1
$$\sqrt{\frac{{x}−\mathrm{1}}{\mathrm{3}{x}+\mathrm{2}}}={u} \\ $$$${u}+\frac{\mathrm{2}}{{u}}=\mathrm{3} \\ $$$${u}^{\mathrm{2}} −\mathrm{3}{u}+\mathrm{2}=\mathrm{0} \\ $$$$\left({u}−\mathrm{2}\right)\left({u}−\mathrm{1}\right)=\mathrm{0}\Rightarrow{u}=\mathrm{2}\:{or}\:{u}=\mathrm{1} \\ $$$${u}=\mathrm{2}\Rightarrow\frac{{x}−\mathrm{1}}{\mathrm{3}{x}+\mathrm{2}}=\mathrm{4}\Rightarrow{x}−\mathrm{1}=\mathrm{12}{x}+\mathrm{8}\Rightarrow{x}=−\frac{\mathrm{9}}{\mathrm{11}} \\ $$$${u}=\mathrm{1}\Rightarrow\frac{{x}−\mathrm{1}}{\mathrm{3}{x}+\mathrm{1}}=\mathrm{1}\Rightarrow{x}−\mathrm{1}=\mathrm{3}{x}+\mathrm{1}\Rightarrow{x}=−\mathrm{1} \\ $$

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