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Question Number 118275 by bramlexs22 last updated on 16/Oct/20

Commented by bramlexs22 last updated on 16/Oct/20

$$f\left(x\right)=x^2,when$$$$(\frac{3}{f\left(1\right)f\left(2\right)}+\frac{5}{f\left(2\right)f\left(3\right)}+\frac{7}{f\left(3\right)f\left(4\right)}+\frac{9}{f\left(4\right)f\left(5\right)}+\frac{11}{f\left(5\right)f\left(6\right)}).x<70$$$$Findthelargestcomplete$$$$solutionoftheinequality.$$$$\left(a\right)64\left(b\right)55\left(c\right)71$$$$\left(d\right)69\left(e\right)74$$

Answered by 1549442205PVT last updated on 16/Oct/20

$$(\frac{3}{\mathrm{f}\left(1\right)\mathrm{f}\left(2\right)}+\frac{5}{\mathrm{f}\left(2\right)\left(\mathrm{f}3\right)}+\frac{7}{\mathrm{f}\left(3\right)\mathrm{f}\left(4\right)}+\frac{9}{\mathrm{f}\left(4\right)\mathrm{f}\left(5\right)}+\frac{11}{\mathrm{f}\left(5\right)\mathrm{f}\left(6\right)})\mathrm{x}<70$$$$\iff (\frac{3}{4}+\frac{5}{36}+\frac{7}{144}+\frac{9}{400}+\frac{11}{900})\mathrm{x}<70$$$$\iff \frac{35}{36}\mathrm{x}<70\iff \mathrm{x}<\frac{70.36}{35}=72$$$$\Rightarrow {\mathrm{x}}_{\max }=71.\mathrm{Hence},\mathrm{choose}\mathrm{c})$$

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