Question

please answer this question​

Answer 1

5^(x+1) + 5^(2-x) = 5^3 + 1

5^x.5 + 5^2/5^x = 126

Suppose, 5^x = y

Then, 5y + 25/y = 126

5y^2 + 25 = 126y

5y^2 - 126y + 25 = 0

5y^2 - (125 + 1)y + 25 = 0

5y^2 - 125y - y + 25 = 0

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

y - 25 = 0. or 5y - 1= 0

y = 25 or y = 1/5

So, 5^x = 25. or. 5^x = 1/5

x = 2. or. x = -1

Thus, x = 2 or -1 .....●●

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Hope it was helpful.