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Question Number 165243 by Zaynal last updated on 28/Jan/22

⌊Find the value of x???⌋ ⌊5x + ((5x)/((5 + 5)^5 )) × (−5x) ÷ 555x −55x ×((5÷5)/5) + x = 555555555555555⌋ ^(proof:z.a)

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\lfloor\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{{x}}???\rfloor \\ $$$$\:\:\:\lfloor\mathrm{5}\boldsymbol{{x}}\:+\:\frac{\mathrm{5}\boldsymbol{{x}}}{\left(\mathrm{5}\:+\:\mathrm{5}\right)^{\mathrm{5}} }\:×\:\left(−\mathrm{5}\boldsymbol{{x}}\right)\:\boldsymbol{\div}\:\mathrm{555}\boldsymbol{{x}}\:−\mathrm{55}\boldsymbol{{x}}\:×\frac{\mathrm{5}\boldsymbol{\div}\mathrm{5}}{\mathrm{5}}\:\:+\:\boldsymbol{{x}}\:=\:\mathrm{555555555555555}\rfloor \\ $$$$\:^{\mathrm{proof}:\mathrm{z}.\mathrm{a}} \\ $$

Answered by alephzero last updated on 28/Jan/22

5x+((5x)/((5+5)^5 ))×(−5x)÷555x−55x× ×((5/5)/5)+x=55555555555555 5x−((10x^2 )/(10×10^4 ))×(1/(555x))−55x×(1/5)+x= =5x−(x/(10^4 ×555))−11x+x= =5x−(x/(10^4 ×555))−10x= =−5x−(x/(5550000))=555555555555555 −((27750001x)/(5550000))=555555555555555 ⇒x=−((5550000×555555555555555)/(27750001))

$$\mathrm{5}{x}+\frac{\mathrm{5}{x}}{\left(\mathrm{5}+\mathrm{5}\right)^{\mathrm{5}} }×\left(−\mathrm{5}{x}\right)\boldsymbol{\div}\mathrm{555}{x}−\mathrm{55}{x}× \\ $$$$×\frac{\mathrm{5}/\mathrm{5}}{\mathrm{5}}+{x}=\mathrm{55555555555555} \\ $$$$\mathrm{5}{x}−\frac{\cancel{\mathrm{10}}{x}^{\cancel{\mathrm{2}}} }{\cancel{\mathrm{10}}×\mathrm{10}^{\mathrm{4}} }×\frac{\mathrm{1}}{\mathrm{555}\cancel{{x}}}−\cancel{\mathrm{55}}{x}×\frac{\mathrm{1}}{\cancel{\mathrm{5}}}+{x}= \\ $$$$=\mathrm{5}{x}−\frac{{x}}{\mathrm{10}^{\mathrm{4}} ×\mathrm{555}}−\mathrm{11}{x}+{x}= \\ $$$$=\mathrm{5}{x}−\frac{{x}}{\mathrm{10}^{\mathrm{4}} ×\mathrm{555}}−\mathrm{10}{x}= \\ $$$$=−\mathrm{5}{x}−\frac{{x}}{\mathrm{5550000}}=\mathrm{555555555555555} \\ $$$$−\frac{\mathrm{27750001}{x}}{\mathrm{5550000}}=\mathrm{555555555555555} \\ $$$$\Rightarrow{x}=−\frac{\mathrm{5550000}×\mathrm{555555555555555}}{\mathrm{27750001}} \\ $$

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