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Question Number 31717 by mondodotto@gmail.com last updated on 13/Mar/18

Answered by Giannibo last updated on 13/Mar/18

$$$$$$$$$$(a,b,c)$$$$c=\lambda b\mathrm{\&}b=\lambda a\Rightarrow c={\lambda }^{2}a$$$$abc=1000\Rightarrow {\lambda }^3{a}^3=1000\Rightarrow \lambda =\frac{10}{a}\left(2\right)$$$$7+c=6+b+\omega \Rightarrow 7+{\lambda }^{2}a=6+\lambda a+\omega \stackrel{\left(1\right)}{\Rightarrow }1+{\lambda }^{2}a=2\lambda a+6-a\stackrel{\left(2\right)}{\Rightarrow }1+\frac{100}{a}=26-a\Rightarrow a^2-25a+100\Rightarrow a=\frac{25\pm 15}{2}=20\mathrm{or}5\left(3\right)$$$$6+b=a+\omega \Rightarrow 6+\lambda a-a=\omega \left(1\right)$$$$\mathrm{If}a=20\Rightarrow \lambda =0.5\Rightarrow b=10\Rightarrow c=5$$$$\mathrm{If}a=5\Rightarrow \lambda =2\Rightarrow b=10\Rightarrow c=20$$

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