Menu Close

solve-x-x-2-4-x-2-6-




Question Number 172007 by Mikenice last updated on 23/Jun/22
solve:  x(√(x^2 +4)) −x^2 =−6
$${solve}: \\ $$$${x}\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}\:−{x}^{\mathrm{2}} =−\mathrm{6} \\ $$
Answered by puissant last updated on 23/Jun/22
x(√(x^2 +4)) = x^2 −6  ⇒ x^2 (x^2 +4)=x^4 −12x^2 +36  ⇒ x^4 +4x^2 =x^4 −12x^2 +36  ⇒ 16x^2 −36=0  ⇒ (4x)^2 −6^2 =0  ⇒ 4x=6  or   4x=−6  ⇒ x=(3/2)     or   x=−(2/3)                 S={−(2/3)  ;  (2/3) }
$${x}\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}\:=\:{x}^{\mathrm{2}} −\mathrm{6} \\ $$$$\Rightarrow\:{x}^{\mathrm{2}} \left({x}^{\mathrm{2}} +\mathrm{4}\right)={x}^{\mathrm{4}} −\mathrm{12}{x}^{\mathrm{2}} +\mathrm{36} \\ $$$$\Rightarrow\:{x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{2}} ={x}^{\mathrm{4}} −\mathrm{12}{x}^{\mathrm{2}} +\mathrm{36} \\ $$$$\Rightarrow\:\mathrm{16}{x}^{\mathrm{2}} −\mathrm{36}=\mathrm{0} \\ $$$$\Rightarrow\:\left(\mathrm{4}{x}\right)^{\mathrm{2}} −\mathrm{6}^{\mathrm{2}} =\mathrm{0} \\ $$$$\Rightarrow\:\mathrm{4}{x}=\mathrm{6}\:\:{or}\:\:\:\mathrm{4}{x}=−\mathrm{6} \\ $$$$\Rightarrow\:{x}=\frac{\mathrm{3}}{\mathrm{2}}\:\:\:\:\:{or}\:\:\:{x}=−\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{S}=\left\{−\frac{\mathrm{2}}{\mathrm{3}}\:\:;\:\:\frac{\mathrm{2}}{\mathrm{3}}\:\right\} \\ $$
Commented by Mikenice last updated on 23/Jun/22
please sir recheck your solution
$${please}\:{sir}\:{recheck}\:{your}\:{solution} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *