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Question Number 154973 by mathdanisur last updated on 23/Sep/21

$$\mathrm{If}\mathrm{x}+\frac{7}{\sqrt{\mathrm{x}}}=50$$$$\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{expression}$$$$\sqrt{\mathrm{x}}-\frac{1}{\sqrt{\mathrm{x}}}=?$$

Answered by mr W last updated on 23/Sep/21

$$lett=\sqrt{x}>0$$$$t^3-50t+7=0$$$$(t-7)(t^2+7t-1)=0$$$$\Rightarrow t=7✓$$$$\Rightarrow t=\frac{-7+\sqrt{53}}{2}✓$$$$\Rightarrow t=\frac{-7-\sqrt{53}}{2}\left(rejected\right)$$$$\sqrt{x}-\frac{1}{\sqrt{x}}=t-\frac{1}{t}=7-\frac{1}{7}=\frac{48}{7}or$$$$\sqrt{x}-\frac{1}{\sqrt{x}}=\frac{-7+\sqrt{53}}{2}-\frac{2}{-7+\sqrt{53}}=-7$$

Commented by mathdanisur last updated on 23/Sep/21

$$\mathrm{Very}\mathrm{nice}\mathrm{solution},\mathbf{S}\mathrm{er}\mathrm{thankyou}$$

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