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Question-151934




Question Number 151934 by john_santu last updated on 24/Aug/21
Answered by MJS_new last updated on 25/Aug/21
3(x^2 −1)=(3+4(√(x+1)))x  ⇒  x_1 =−((11)/(18))+((√(13))/(18))  x_2 =(5/2)+((√(13))/2)  ⇒  answer is −1≤x≤−((11)/(18))+((√(13))/(18))∨x≥(5/2)+((√(13))/2)
$$\mathrm{3}\left({x}^{\mathrm{2}} −\mathrm{1}\right)=\left(\mathrm{3}+\mathrm{4}\sqrt{{x}+\mathrm{1}}\right){x} \\ $$$$\Rightarrow \\ $$$${x}_{\mathrm{1}} =−\frac{\mathrm{11}}{\mathrm{18}}+\frac{\sqrt{\mathrm{13}}}{\mathrm{18}} \\ $$$${x}_{\mathrm{2}} =\frac{\mathrm{5}}{\mathrm{2}}+\frac{\sqrt{\mathrm{13}}}{\mathrm{2}} \\ $$$$\Rightarrow \\ $$$$\mathrm{answer}\:\mathrm{is}\:−\mathrm{1}\leqslant{x}\leqslant−\frac{\mathrm{11}}{\mathrm{18}}+\frac{\sqrt{\mathrm{13}}}{\mathrm{18}}\vee{x}\geqslant\frac{\mathrm{5}}{\mathrm{2}}+\frac{\sqrt{\mathrm{13}}}{\mathrm{2}} \\ $$
Commented by john_santu last updated on 25/Aug/21
short cut
$$\mathrm{short}\:\mathrm{cut} \\ $$

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