Question Number 24661 by behi.8.3.4.17@gmail.com last updated on 24/Nov/17
Commented by prakash jain last updated on 25/Nov/17
$$\mathrm{Answer}\:\mathrm{from}\:\mathrm{wolfram}\:\mathrm{alpha} \\ $$
Commented by prakash jain last updated on 25/Nov/17
Answered by jota+ last updated on 05/Dec/17
$$\frac{{x}^{\mathrm{2}} }{{x}+\mathrm{1}}+\sqrt{{x}}=\mathrm{1} \\ $$$$\frac{{x}^{\mathrm{2}} }{{x}+\mathrm{1}}=\mathrm{1}−\sqrt{{x}} \\ $$$${x}^{\mathrm{2}} =\left({x}+\mathrm{1}\right)\left(\mathrm{1}−\sqrt{{x}}\right) \\ $$$${x}^{\mathrm{2}} \left(\mathrm{1}+\sqrt{{x}}\right)=\left(\mathrm{1}+{x}\right)\left(\mathrm{1}−{x}\right) \\ $$$$\mathrm{2}{x}^{\mathrm{2}} +{x}^{\mathrm{2}} \sqrt{{x}}=\mathrm{1}. \\ $$$${x}\approx\frac{−\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}. \\ $$