Question

9x2-10x+1>0 ??? Lzkcioskxoxoxo хелп

Answer 1

Ответ:

Объяснение:

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Answer 2

Ответ:

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Объяснение:

Answer 3

To solve the inequality 9x^2 - 10x + 1 > 0, we can use the method of factoring and sign analysis. Here's the step-by-step process:

Step 1: Factor the quadratic expression. To factor 9x^2 - 10x + 1, we look for two numbers whose product is (9)(1) = 9 and whose sum is -10. The two numbers are -9 and -1.

9x^2 - 10x + 1 = 9x^2 - 9x - x + 1 = 9x(x - 1) - 1(x - 1) = (9x - 1)(x - 1)

Step 2: Find the critical points. Set each factor equal to zero and solve for x:

9x - 1 = 0 => 9x = 1 => x = 1/9

x - 1 = 0 => x = 1

Step 3: Create a sign chart.

We have three intervals to consider: Interval 1: x < 1/9 Interval 2: 1/9 < x < 1 Interval 3: x > 1

Step 4: Test a value in each interval.

• For Interval 1, choose x = 0 (a value less than 1/9): 9x^2 - 10x + 1 = 9(0)^2 - 10(0) + 1 = 1 (positive)

• For Interval 2, choose x = 1/2 (a value between 1/9 and 1): 9x^2 - 10x + 1 = 9(1/2)^2 - 10(1/2) + 1 = 9/4 - 5 + 1 = 9/4 - 4/4 = 5/4 (positive)

• For Interval 3, choose x = 2 (a value greater than 1): 9x^2 - 10x + 1 = 9(2)^2 - 10(2) + 1 = 36 - 20 + 1 = 17 (positive)

Step 5: Determine the solution.

Since the inequality is greater than zero (>) and the expression is positive in all three intervals, the solution is the combination of all the intervals:

x < 1/9 OR 1/9 < x < 1 OR x > 1

Thus, the solution to the inequality 9x^2 - 10x + 1 > 0 is: x < 1/9 or 1/9 < x < 1 or x > 1.