Question

25power(2x-1) +100=5power(2x-1)

Answer 1

$\bull \: \: \: { \underline{\rm \bold{Given :}}}$

$\mapsto \: \: \: \: \sf {25}^{(2x - 1)} + 100 = {5}^{(2x - 1)}$

$\bull \: \: \: { \underline{\rm \bold{Solution \: :}}}$

$\: \: \: \: \: \: \: \: \: \: \: \sf {25}^{(2x - 1)} + 100 = {5}^{(2x - 1)}$

$\implies \: \sf {5}^{2(2x - 1)} - {5}^{(2x - 1)} + 100 = 0$

${ \sf \: let, \: { {5}^{(2x - 1)} = a}}$

$\implies \: \sf \: {a}^{2} - a + 100 = 0$

$\implies \sf a = \frac{ - ( -1 ) ± \sqrt{ {( - 1)}^{2} - 4 \times 1 \times 100} }{2 \times 1}$

$\therefore \underline{\boxed{\sf \: roots \: are \: imaginary }}$

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HOPE THIS IS HELPFUL...