Question

решите неравенство: (x-3)√5-2x<0

Answer 1

(x-3)√5 - 2x < 0

√5 * x - 3√5 - 2x <0

x(√5 - 2) < 3√5

В силу того, что √5 > 2, то (√5 - 2) > 0, значит, знак при делении на это выражение мы не меняем.

Выполним деление:

3√5 / (√5 - 2) = 3√5(√5 + 2) / (√5 - 2)(√5 + 2) = 3√5(√5+2) / (√5)² - 4 = 15 + 6√5 / 5-4 = 15 + 6√5

Значит,

x < 15 + 6√5

Answer 2

To solve the inequality (x-3)√5-2x<0, we can use the following steps:

- First, we can isolate x by adding 2x to both sides and dividing by √5. This gives us x-3<2x/√5. - Next, we can subtract x from both sides and multiply by √5. This gives us -3√5<√5x. - Finally, we can divide by √5 and get -3

Therefore, the solution set is (-3, ∞), which means that x can be any real number greater than -3.

You can also check the solution using an online calculator or a graph. Here is a graph of the inequality: