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Question Number 75176 by 21042004 last updated on 08/Dec/19

P=(√(25x−50))−14(√((x−2)/4))+(√(9x−18)),  x≥2  a) Simplify the equation  b) Find x if P=3

$$\mathrm{P}=\sqrt{\mathrm{25}{x}−\mathrm{50}}−\mathrm{14}\sqrt{\frac{{x}−\mathrm{2}}{\mathrm{4}}}+\sqrt{\mathrm{9}{x}−\mathrm{18}},\:\:{x}\geqslant\mathrm{2} \\ $$$$\left.\mathrm{a}\right)\:\mathrm{Simplify}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\left.\mathrm{b}\right)\:\mathrm{Find}\:\mathrm{x}\:\mathrm{if}\:\mathrm{P}=\mathrm{3} \\ $$

Answered by Kunal12588 last updated on 08/Dec/19

P=(√(25(x−2)))−14((√(x−2))/(√4))+(√(9(x−2)))  =(√(x−2))(5−7+3)  =(√(x−2))  P=3  ⇒(√(x−2))=3  ⇒x=11

$${P}=\sqrt{\mathrm{25}\left({x}−\mathrm{2}\right)}−\mathrm{14}\frac{\sqrt{{x}−\mathrm{2}}}{\sqrt{\mathrm{4}}}+\sqrt{\mathrm{9}\left({x}−\mathrm{2}\right)} \\ $$$$=\sqrt{{x}−\mathrm{2}}\left(\mathrm{5}−\mathrm{7}+\mathrm{3}\right) \\ $$$$=\sqrt{{x}−\mathrm{2}} \\ $$$${P}=\mathrm{3} \\ $$$$\Rightarrow\sqrt{{x}−\mathrm{2}}=\mathrm{3} \\ $$$$\Rightarrow{x}=\mathrm{11} \\ $$

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