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given-2017x-2-4034x-17-2017x-2-4034x-3-10-then-find-the-value-x-2-2x-




Question Number 21426 by x² – y²@gmail.com last updated on 23/Sep/17
given (√(2017x^2  + 4034x + 17)) + (√(2017x^2  + 4034x − 3)) = 10,  then find the value x^2  + 2x.
$$\mathrm{given}\:\sqrt{\mathrm{2017}{x}^{\mathrm{2}} \:+\:\mathrm{4034}{x}\:+\:\mathrm{17}}\:+\:\sqrt{\mathrm{2017}{x}^{\mathrm{2}} \:+\:\mathrm{4034}{x}\:−\:\mathrm{3}}\:=\:\mathrm{10}, \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}. \\ $$
Answered by $@ty@m last updated on 23/Sep/17
Let x^2  + 2x=y  The given equation:  (√(2017y+17))+(√(2017y−3))=10  (√(2017y+17))=10−(√(2017y−3))  Squarring  2017y+17=100+2017y−3−20(√(2017y−3))  20(√(2017y−3))=80  (√(2017y−3))=4  2017y−3=16  y=((19)/(2017))  x^2  + 2x=((19)/(2017))
$${Let}\:{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}={y} \\ $$$${The}\:{given}\:{equation}: \\ $$$$\sqrt{\mathrm{2017}{y}+\mathrm{17}}+\sqrt{\mathrm{2017}{y}−\mathrm{3}}=\mathrm{10} \\ $$$$\sqrt{\mathrm{2017}{y}+\mathrm{17}}=\mathrm{10}−\sqrt{\mathrm{2017}{y}−\mathrm{3}} \\ $$$${Squarring} \\ $$$$\mathrm{2017}{y}+\mathrm{17}=\mathrm{100}+\mathrm{2017}{y}−\mathrm{3}−\mathrm{20}\sqrt{\mathrm{2017}{y}−\mathrm{3}} \\ $$$$\mathrm{20}\sqrt{\mathrm{2017}{y}−\mathrm{3}}=\mathrm{80} \\ $$$$\sqrt{\mathrm{2017}{y}−\mathrm{3}}=\mathrm{4} \\ $$$$\mathrm{2017}{y}−\mathrm{3}=\mathrm{16} \\ $$$${y}=\frac{\mathrm{19}}{\mathrm{2017}} \\ $$$${x}^{\mathrm{2}} \:+\:\mathrm{2}{x}=\frac{\mathrm{19}}{\mathrm{2017}} \\ $$

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