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Question-65911




Question Number 65911 by Masumsiddiqui399@gmail.com last updated on 05/Aug/19
Commented by Prithwish sen last updated on 06/Aug/19
x(x+1)(x+2)(x+3)=180×182                                               =12×13×14×15  ∵x is a positive real number  ∴(x+3)=15
$$\mathrm{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)=\mathrm{180}×\mathrm{182} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{12}×\mathrm{13}×\mathrm{14}×\mathrm{15} \\ $$$$\because\mathrm{x}\:\mathrm{is}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{number} \\ $$$$\therefore\left(\mathrm{x}+\mathrm{3}\right)=\mathrm{15} \\ $$