Question

9^x-4-3^x-4(9-x^2)-9x^2 >0

Answer 1

Ответ:x>6

Пошаговое объяснение:

раскроем скобки 9^x-4-3^x-4 *9+3^x-4 *x^2-9x^2>0, введем переменную

t=3^x-4, t>0,  имеем  t^2-9t+t*x^2-9x^2>0,  группировка,   t(t-9)+x^2(t-9)>0,

(t-9)(t+x^2)>0,  разделим на t+x^2>0,  получим  t-9>0,  обратная замена

3^x-4>9, 3^x-4>3^2,  x-4>2,  x>6

Answer 2

To solve the inequality $9^x-4-3^x-4(9-x^2)-9x^2>0$, we'll first simplify it and then find the values of $x$ that satisfy the inequality. Let's go step by step:

Step 1: Simplify the expression $9^x - 4 - 3^x - 4(9 - x^2) - 9x^2 > 0$

Step 2: Combine like terms $9^x - 3^x - 4(9 - x^2) - 9x^2 > 4$

Step 3: Expand the expression inside the parentheses $9^x - 3^x - 36 + 4x^2 - 9x^2 > 4$

Step 4: Combine the $x^2$ terms $9^x - 3^x - 5x^2 - 36 > 4$

Step 5: Move the constant term to the right side $9^x - 3^x - 5x^2 > 40$

At this point, we cannot find an exact analytical solution for this inequality. However, we can use numerical methods or graphical representation to find approximate solutions.

If you are looking for a numerical solution, you can use numerical methods like Newton-Raphson or the bisection method to approximate the solutions of the equation $9^x - 3^x - 5x^2 = 40$.

If you are looking for a graphical solution, you can plot the functions $y = 9^x - 3^x - 5x^2$ and $y = 40$ on the same graph and find the values of $x$ where the first function is greater than the second one.

Keep in mind that without a specific range or interval for $x$, there may be multiple solutions to this inequality.