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Question Number 183846 by Michaelfaraday last updated on 30/Dec/22

Answered by MJS_new last updated on 31/Dec/22

$$1.x=0\Rightarrow \sqrt{x-\sqrt{x}}=0$$$$2.x>0$$$$t=\sqrt{x-\sqrt{x}}⩾0\Rightarrow x=\frac{{(1\pm \sqrt{4t^2+1})}^2}{4}$$$$\mathrm{insert}\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{equation}\mathrm{to}\mathrm{get}$$$$t=7$$

Commented by Michaelfaraday last updated on 31/Dec/22

$$okaythankbutpleasegivemoredetail$$$$onit.$$

Commented by MJS_new last updated on 31/Dec/22

$$\mathrm{I}\mathrm{give}\mathrm{the}\mathrm{path}\mathrm{you}\mathrm{do}\mathrm{the}\mathrm{writing}\mathrm{work}.{\mathrm{it}}^{\prime }\mathrm{s}$$$$\mathrm{easy}...$$

Commented by Michaelfaraday last updated on 31/Dec/22

$$okaysir$$

Answered by mr W last updated on 31/Dec/22

$$x^2-50x=49\sqrt{x}$$$$letu=\sqrt{x}⩾0$$$$u^4-50u^2=49u$$$$u=0:$$$$\Rightarrow \sqrt{x-\sqrt{x}}=\sqrt{u^2-u}=0✓$$$$u\ne 0:$$$$\Rightarrow u^3-50u-49=0$$$$\Rightarrow u^3+u^2-u^2-u-49u-49=0$$$$\Rightarrow (u+1)(u^2-u-49)=0$$$$\Rightarrow u^2-u=49$$$$\Rightarrow \sqrt{x-\sqrt{x}}=\sqrt{u^2-u}=\sqrt{49}=7✓$$

Commented by Michaelfaraday last updated on 31/Dec/22

$$thankssir$$

Answered by manxsol last updated on 31/Dec/22

$$\sqrt{x-\sqrt{x}}=\sqrt{\frac{x^2-x}{x+\sqrt{x}}}=7$$$$x^2-x=49x+49\sqrt{x}=49(x+\sqrt{x})$$$$\frac{x^2-x}{x+\sqrt{x}}=49$$

Commented by Michaelfaraday last updated on 31/Dec/22

$$thankssir$$

Answered by CElcedricjunior last updated on 31/Dec/22

$${\mathit{x}}^2-50\mathit{x}-49\sqrt{\mathit{x}}=0$$$$\mathit{p}\mathit{o}\mathit{s}\mathit{o}\mathit{n}\mathit{s}\mathit{t}=\sqrt{\mathit{x}}$$$$=>{\mathit{t}}^4-50{\mathit{t}}^2-49\mathit{t}=0$$$$=>\mathit{t}=0\mathit{o}\mathit{u}$$$${\mathit{t}}^3-50\mathit{t}-49=0$$$$(\mathit{t}+1)({\mathit{t}}^2-\mathit{t}-49)=0$$$$\mathit{t}=-1\mathit{o}\mathit{u}{\mathit{t}}^2-\mathit{t}-49=0$$$$\mathbf{\Delta }=1+196=197$$$$\mathit{t}=0\mathit{o}\mathit{u}\mathit{t}=-1\mathit{o}\mathit{u}\mathit{t}=\frac{1\mp \sqrt{197}}{2}$$$$\mathit{t}=\sqrt{\mathit{x}}=>\mathit{x}={\left(\frac{1+\sqrt{197}}{2}\right)}^2$$$$=>$$$$\sqrt{\mathit{x}-\sqrt{\mathit{x}}}=\sqrt{{\left(\frac{1+\sqrt{197}}{2}\right)}^2-\frac{1+\sqrt{197}}{2}}$$$$=\sqrt{\frac{198-2+2\sqrt{197}-2\sqrt{197}}{4}}$$$$=\sqrt{\frac{196}{4}}=\sqrt{49}=7$$$$=>\sqrt{\mathit{x}-\sqrt{\mathit{x}}}=7$$$$========================$$$$............lecelebrecedricjunior...........$$$$=====================$$$$$$$$$$$$($$

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