Question

Solve : 5^(x+1) + 5^(2-x) = 5³+1

Answer 1

Hope it will help you !!

Answer 2

Hey mate,☺☺☺

Here is your answer...✨✨✨

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${5}^{x + 1} + {5}^{2 - x} = {5}^{3} + 1$

${5}^{x + 1} + {5}^{2 - x} = 126$

${5}^{x} .5 + {5}^{2} . {5}^{ - x } =126$

${5}^{x} .5 + \frac{25}{ {5}^{x} } = 126$

$5y + \frac{25}{y} = 126 \: \: \: \: where \: {5}^{x} = y$

$5 {y}^{2} + 25 = 126y$

$5 {y}^{2} - 126y + 25 = 0$

$5 {y}^{2} - 125y - y + 25 = 0$

$5y(y - 25) - 1(y - 25) = 0$

$(y - 25)(5y - 1) = 0$

$y - 25 = 0 \: \: \: or \: \: \: 5y - 1 = 0$

$y = 25 \: \: \: \: or \: \: \: \: y = \frac{1}{5}$

${5}^{x} = 25 = {5}^{2} \: \: \: \: \: or \: \: \: \: \: {5}^{x} = {5}^{ - 1}$

$x = 2 \: \: \: \: \: or \: \: \: \: \: x = - 1$

Hence, 2 and -1 are the roots of the given equation....

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Hope this will help you...✨✨✨

Keep Asking..✌✌✌

❤❤❤ THANKS....❤❤❤