Question

25^(x)-26×(5^x)+25 = 0

Answer 1

Чтобы решить это уравнение нужно произвести замену переменных:

Answer 2

This is a quadratic equation in terms of 5^x. Let's substitute y = 5^x to simplify the equation:

25^(x) - 26 × (5^x) + 25 = 0

(5^x)^2 - 26 × 5^x + 25 = 0 (substituting y = 5^x)

Now we can solve this quadratic equation by using the quadratic formula:

y = [-b ± sqrt(b^2 - 4ac)] / 2a

where a = 1, b = -26, and c = 25. Substituting these values, we get:

y = [-(-26) ± sqrt((-26)^2 - 4(1)(25))] / 2(1)

y = [26 ± sqrt(676 - 100)] / 2

y = [26 ± sqrt(576)] / 2

y = [26 ± 24] / 2

y = 25 or y = 1

Now we can substitute back to get the value of x:

If y = 25, then 5^x = 25, which means x = 2.

If y = 1, then 5^x = 1, which means x = 0.

Therefore, the solutions to the equation are x = 2 and x = 0.