Question

При каких значениях параметра а уравнение (√х-а)(9х-16)=0 имеет единственное решение?

Answer 1

Ответ:

а=√х

Пошаговое объяснение:

Answer 2

Values of Parameter 'a' for Unique Solution of the Equation (√x - a)(9x - 16) = 0

To find the values of the parameter 'a' for which the equation (√x - a)(9x - 16) = 0 has a unique solution, we need to determine when the equation has only one solution.

The equation (√x - a)(9x - 16) = 0 can be rewritten as two separate equations:

1. √x - a = 0 2. 9x - 16 = 0

Let's solve each equation separately:

1. √x - a = 0 - Adding 'a' to both sides of the equation, we get √x = a. - Squaring both sides of the equation, we get x = a^2.

2. 9x - 16 = 0 - Adding 16 to both sides of the equation, we get 9x = 16. - Dividing both sides of the equation by 9, we get x = 16/9.

Therefore, the equation (√x - a)(9x - 16) = 0 has a unique solution when the values of 'a' satisfy the following conditions: - a^2 = 16/9

To find the values of 'a', we can take the square root of both sides of the equation: - √(a^2) = √(16/9) - a = ±4/3

Hence, the equation (√x - a)(9x - 16) = 0 has a unique solution when the parameter 'a' takes the values of a = 4/3 or a = -4/3.