X+1≥√7x-3 √x+√2x-6>10 √18-2x‹3 √10-√x-5<27

Предыдущий
вопрос Следующий
вопрос

x+1 ≥ √(7x-3)
To solve this inequality, first square both sides to get rid of the square root:
(x+1)² ≥ 7x-3
x² + 2x + 1 ≥ 7x - 3
x² - 5x + 4 ≥ 0
(x-4)(x-1) ≥ 0
The solution for this inequality is x ≤ 1 or x ≥ 4.

√x + √(2x-6) > 10
To solve this inequality, square both sides to eliminate the square root:
(x) + 2√x(2x-6) + (2x-6) > 100
x + 4x√(2x-6) + 2x - 6 > 100
5x + 4x√(2x-6) > 106
4x√(2x-6) > 106 - 5x
Squaring both sides we get:
16x²(2x-6) > (106 - 5x)²
After simplifying and solving the above inequality, we get the range of values for x.

√18 - 2x < 3
To solve this inequality, we first simplify:
√18 - 2x < 3
√18 < 2x + 3
18 < (2x + 3)²
Solving the above inequality will give the range of values for x.

√10 - √(x-5) < 27
To solve this inequality, we first square both sides to get rid of the square root:
√10 - √(x-5) < 27
10 - 2√10√(x-5) + (x-5) < 729
15 - 2√10√(x-5) < 729
2√10√(x-5) > -714
After squaring both sides, we can simplify and solve this inequality to get the range of values for x.