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Question Number 99227 by Algoritm last updated on 19/Jun/20

Commented by Algoritm last updated on 19/Jun/20

thank you

$$\mathrm{thank}\:\mathrm{you} \\ $$

Commented by MJS last updated on 19/Jun/20

(I) x(√(10−x^2 ))=x^2 −6 x^2 (10−x^2 )=(x^2 −6)^2 −2x^4 +22x^2 −36=0 x^4 −11x^2 −18=0 (x^2 −9)(x^2 −2)=0 now test all solutions if they fit (I) ⇒ x_1 =−(√2)∧x_2 =3

$$\left(\mathrm{I}\right)\:\:{x}\sqrt{\mathrm{10}−{x}^{\mathrm{2}} }={x}^{\mathrm{2}} −\mathrm{6} \\ $$$${x}^{\mathrm{2}} \left(\mathrm{10}−{x}^{\mathrm{2}} \right)=\left({x}^{\mathrm{2}} −\mathrm{6}\right)^{\mathrm{2}} \\ $$$$−\mathrm{2}{x}^{\mathrm{4}} +\mathrm{22}{x}^{\mathrm{2}} −\mathrm{36}=\mathrm{0} \\ $$$${x}^{\mathrm{4}} −\mathrm{11}{x}^{\mathrm{2}} −\mathrm{18}=\mathrm{0} \\ $$$$\left({x}^{\mathrm{2}} −\mathrm{9}\right)\left({x}^{\mathrm{2}} −\mathrm{2}\right)=\mathrm{0} \\ $$$$\mathrm{now}\:\mathrm{test}\:\mathrm{all}\:\mathrm{solutions}\:\mathrm{if}\:\mathrm{they}\:\mathrm{fit}\:\left(\mathrm{I}\right) \\ $$$$\Rightarrow\:{x}_{\mathrm{1}} =−\sqrt{\mathrm{2}}\wedge{x}_{\mathrm{2}} =\mathrm{3} \\ $$

Answered by MJS last updated on 19/Jun/20

−(√2)<x<3

$$−\sqrt{\mathrm{2}}<{x}<\mathrm{3} \\ $$

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