Question

ПОМОГИТЕ ПОЖАЛУЙСТА! Я НЕ УВЕРЕНА В СВОЕМ ОТВЕТЕ!! Довебіть що при будьякому значенні змінної даний вираз набуває тільки додатних значень , якого найменшого значення і при якому значенні х набуває цей вираз? Х²-8х+17 Х²+10х+26

Answer 1

Х²-8х+17=(х-4)²+1 при любом х принимает положительные значения
1 наименьшее значение выражения, при х=4
х²+10х+26=(х+5)²+1 примает только положительные значения при любом х 
1 наименьшее значение, достигается при х=-5

Answer 2

Expression Analysis:

The given expression is: x² - 8x + 17 + x² + 10x + 26.

To determine the minimum value of this expression and the corresponding value of x, we can simplify and analyze the expression.

Simplification:

Let's simplify the expression by combining like terms:

x² - 8x + 17 + x² + 10x + 26

Combining the x² terms, we get:

2x² - 8x + 17 + 10x + 26

Combining the x terms, we get:

2x² + 2x + 43

Now, we have a quadratic expression in the form of ax² + bx + c.

Minimum Value:

To find the minimum value of a quadratic expression, we can use the formula x = -b / (2a), where a, b, and c are the coefficients of the quadratic expression.

In our case, a = 2, b = 2, and c = 43.

Using the formula, we can find the value of x:

x = -b / (2a) = -2 / (2 * 2) = -1/2

Therefore, the expression x² - 8x + 17 + x² + 10x + 26 has its minimum value when x = -1/2.

Verification:

To verify that the expression only takes positive values for any other value of x, we can substitute different values of x into the expression and observe the results.

Let's substitute x = -1/2 into the expression:

(-1/2)² - 8(-1/2) + 17 + (-1/2)² + 10(-1/2) + 26

Simplifying this expression, we get:

1/4 + 4 + 17 + 1/4 - 5 + 26 = 48.5

As we can see, the expression evaluates to a positive value when x = -1/2.

Therefore, we can conclude that for any value of x, the expression x² - 8x + 17 + x² + 10x + 26 only takes positive values, and its minimum value occurs when x = -1/2.