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Question Number 194113 by Rupesh123 last updated on 28/Jun/23

Answered by Subhi last updated on 28/Jun/23

((a(a−1)(a−2).....)/(a(a−2)(a−4).....)).((b(b−2)(b−4)...)/(b(b−1)(b−2)....)) = (((a−1)(a−3)(a−5).....)/((b−1)(b−3)(b−5).....)) 24 can be the multiplication of n, n+2 (4),(6) a−1 = 6 , a−3 = 4 ⇛ a = 7 a−5 = 2 = (b−1) ⇛ b = 3 a + b = 10

$$ \\ $$$$\frac{{a}\left({a}−\mathrm{1}\right)\left({a}−\mathrm{2}\right).....}{{a}\left({a}−\mathrm{2}\right)\left({a}−\mathrm{4}\right).....}.\frac{{b}\left({b}−\mathrm{2}\right)\left({b}−\mathrm{4}\right)...}{{b}\left({b}−\mathrm{1}\right)\left({b}−\mathrm{2}\right)....} \\ $$$$\:=\:\frac{\left({a}−\mathrm{1}\right)\left({a}−\mathrm{3}\right)\left({a}−\mathrm{5}\right).....}{\left({b}−\mathrm{1}\right)\left({b}−\mathrm{3}\right)\left({b}−\mathrm{5}\right).....}\:\:\:\: \\ $$$$\mathrm{24}\:{can}\:{be}\:{the}\:{multiplication}\:{of}\:{n},\:{n}+\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{4}\right),\left(\mathrm{6}\right) \\ $$$${a}−\mathrm{1}\:=\:\mathrm{6}\:,\:{a}−\mathrm{3}\:=\:\mathrm{4}\:\:\Rrightarrow\:{a}\:=\:\mathrm{7} \\ $$$${a}−\mathrm{5}\:=\:\mathrm{2}\:=\:\left({b}−\mathrm{1}\right)\:\:\Rrightarrow\:{b}\:=\:\mathrm{3} \\ $$$${a}\:+\:{b}\:=\:\mathrm{10} \\ $$

Commented by Rupesh123 last updated on 28/Jun/23

Perfect ��

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