Question

Скільки коренів має рівняння (x-5)⁷:(x-5)⁵=-4

Answer 1

.........................

Answer 2

We can simplify the equation by canceling out the common factors in the numerator and denominator:

(x-5)⁷/(x-5)⁵ = -4

Since the bases are the same (x-5), we can subtract the exponents:

(x-5)² = -4

Expanding the equation, we get:

x² + 25 - 10x = -4

Moving all the terms to one side, we have:

x² - 10x + 29 = 0

This is a quadratic equation in the form ax² + bx + c = 0, where a = 1, b = -10, and c = 29.

To find the roots of the equation, we can apply the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values, we have:

x = (-(-10) ± √((-10)² - 4(1)(29))) / (2(1))

Simplifying,

x = (10 ± √(100 - 116)) / 2

x = (10 ± √(-16)) / 2

Since the discriminant (b² - 4ac) is negative, the square root of a negative number is not a real number. Therefore, the equation has no real roots.

In conclusion, the equation (x-5)⁷/(x-5)⁵ = -4 has no real roots.