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  • The sum of three consecutive numbers in GP is 39 and their product is 729 then find all three numbers

The sum of three consecutive numbers in G.P. is 39 and their product is 729 then find all three numbers ?

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@Vishal

\\Let\:three\:no.\:be\:\frac{a}{r},a,{a}{r}\\ Product\:\:a^3=729\Rightarrow a=9\\ \frac{a}{r}+a+ar=39\Rightarrow \frac{9}{r}+9+9r=39\\9r^2-30r+9=0\\roots\:of\:quardratic\:equation:ax^2+bx+c=0\\ \alpha,\beta=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\roots\:of\:the\:equation\:are,r_1,r_2=\:\frac{30\pm\sqrt{576}}{18}=\frac{30\pm{24}}{18}\\You\:got\:value\:a\:and\:r.\:I\:hope\:further\:you\:can\:solve\:by\:yourself.

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himanshu.meshram

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