Question

if the sum of three numbers in a G.P. is 26 and the sum of products taken two at a time is 156 find the numbers are ​

Answer 1

$\large \bold \green{ \underline{answer}} \\ \\ \implies \bold{the \: \: numbers \: \: are \: \: = 2 \: \: \: \: 6 \: \: \: \: 18} \\ \\ \implies \bold \orange{ \underline{explanation}} \\ \\ \implies \bold{ \underline{given}} \\ \\ \implies \bold{sum \: \: of \: \: three \: \: number \: \: of \: \: gp \: = 26} \\ \\ \implies \bold{sum \: \: of \: \: products \: \: taken \: \: two \: \: at \: \: a \: \: time \: = 156} \\ \\ \implies \bold { \underline \green{find \: }} \\ \\ \implies \bold{the \: \: numbers \: \: are \: } \\ \\ \implies \bold{sum \: \: of \: \: three \: number \: \: of \: \: gp \: = } \\ \\ \implies \bold{ \frac{a}{r} \: \: \: a \: \: \: ar \: \: = \: three \: \: number \: \: of \: \: gp } \\ \\ \implies \bold{a( \frac{1}{r} + 1 + r) = 26}.......(1) \\ \\ \implies \bold{ {a}^{2}( \frac{1}{r} + 1 + r) = 156......(2) } \\ \\ \implies \bold{dividing \: \: equation \: \: (1) \: \: by \: \: (2) } \\ \\ \implies \bold{we \: \: get \: \: a \: = 6} \\ \\ \implies \bold{put \: \: the \: \: value \: \: of \: \: a \: \: \: in \: \: equation \: \: (1)} \\ \\ \implies \bold{we \: \: get \: \: r \: = 3} \\ \\ \implies \bold{ \frac{a}{r} = \frac{6}{3} = 2} \\ \\ \implies \bold{a \: \: = 6} \\ \\ \implies \bold{ar \: = 18} \\ \\ \implies \bold \therefore \green{these \: \: numbers \: \: are \: \: \: \: 2 \: \: \: \: 6 \: \: \: \: \: 18}$