Question

1) x2 + 70 > 0 2) x2 − 70 > 0 3) x2 + 70 < 0 4) x2 − 70 < 0 Ука­жи­те не­ра­вен­ство, ре­ше­ни­ем ко­то­ро­го яв­ля­ет­ся любое число. и решение пж)

Answer 1

1) x^2 + 70 > 0
x^2>-70 Это неравенство верно при любом числе х, т.к. число в квадрате больше 0
2) x^2 − 70 > 0
х^2>70 Верно, но не при любом значении х
3) x^2 + 70 < 0
x^2<-70, Это неравенство неверно, т.к. число в квадрате больше 0
4) x^2 − 70 < 0
х^2<70, Это неравенство верно, но не при любом значении х
Ответ: 1

Answer 2

1) x^2 + 70 > 0 2) x^2 - 70 > 0 3) x^2 + 70 < 0 4) x^2 - 70 < 0

Let's solve each inequality one by one:

1) x^2 + 70 > 0: To solve this inequality, we need to find the values of x for which the expression x^2 + 70 is greater than zero. We can start by subtracting 70 from both sides: x^2 > -70

Since the square of any real number is always non-negative, there are no real solutions to this inequality. This means that x^2 + 70 will always be greater than zero for any value of x.

2) x^2 - 70 > 0: To solve this inequality, we need to find the values of x for which the expression x^2 - 70 is greater than zero. We can start by adding 70 to both sides: x^2 > 70

To find the values of x, we can take the square root of both sides, remembering to consider both the positive and negative square roots: x > sqrt(70) or x < -sqrt(70)

So, the solution to this inequality is x > sqrt(70) or x < -sqrt(70). This means that any number greater than the square root of 70 or any number less than the negative square root of 70 will satisfy the inequality.

3) x^2 + 70 < 0: To solve this inequality, we need to find the values of x for which the expression x^2 + 70 is less than zero. We can start by subtracting 70 from both sides: x^2 < -70

Again, since the square of any real number is always non-negative, there are no real solutions to this inequality. This means that x^2 + 70 will always be greater than zero for any value of x.

4) x^2 - 70 < 0: To solve this inequality, we need to find the values of x for which the expression x^2 - 70 is less than zero. We can start by adding 70 to both sides: x^2 < 70

To find the values of x, we can take the square root of both sides, remembering to consider both the positive and negative square roots: x < sqrt(70) or x > -sqrt(70)

So, the solution to this inequality is x < sqrt(70) or x > -sqrt(70). This means that any number less than the square root of 70 or any number greater than the negative square root of 70 will satisfy the inequality.

In summary: 1) There is no solution to x^2 + 70 > 0. 2) The solution to x^2 - 70 > 0 is x > sqrt(70) or x < -sqrt(70). 3) There is no solution to x^2 + 70 < 0. 4) The solution to x^2 - 70 < 0 is x < sqrt(70) or x > -sqrt(70).