Question

3×4ˣ + 2*9ˣ - 5*6ˣ < 0

Answer 1

Ответ:

x=(0;1)

Пошаговое объяснение:

делим на 6^x (положительное)

3*(2/3)^x+2*(3/2)^x-5<0

замена t=(2/3)^x (положительное)

3*t+2/t-5<0

3*t^2-5t+2<0

D=25-24=1

t=(5+-1)/6=1;2/3

  +               -             +

--------(2/3)-----------1--------

t=(2/3;1)

2/3^x=1 => x=0

2/3^x=2/3 => x=1

x=(0;1)

Answer 2

To solve the inequality 3×4ˣ + 29ˣ - 56ˣ < 0, you can use some algebraic techniques. Let's work through it step by step.

First, notice that all the terms in the inequality have exponential expressions with the same base, which is 6. So, let's rewrite the inequality with a common base:

3(6^x) + 2(6^x) - 5(6^x) < 0

Now, you can combine the like terms on the left side of the inequality:

(3 + 2 - 5)(6^x) < 0

(0)(6^x) < 0

Since 0 times any number is still 0, we have:

0 < 0

This is not a true statement. In fact, 0 is not less than 0; they are equal. Therefore, there are no values of x that satisfy the given inequality. In other words, there is no solution to the inequality 3×4ˣ + 29ˣ - 56ˣ < 0.