Question

X^2-(9-x)^2>-2x решить неравенство

Answer 1

x²-(9-x)²>-2x

x²-(81-18x+x²)>-2x

x²-81+18x-x²>-2x

-81+18x>-2x

20x>81   |÷20

x>4,05.

Answer 2

первый и второй вариант ответа

$x > \frac{81}{20} \\ ( \frac{80}{20} \infty )$

Answer 3

To solve the inequality $x^2 - (9 - x)^2 > -2x$, we'll first simplify it and then find the critical points to determine the solution regions.

Step 1: Simplify the inequality. Expand $(9 - x)^2$ to $81 - 18x + x^2$ and rewrite the inequality:

$x^2 - (81 - 18x + x^2) > -2x$

Now, simplify further:

$x^2 - 81 + 18x - x^2 > -2x$

Step 2: Cancel out like terms. The $x^2$ terms cancel out:

$18x - 81 > -2x$

Step 3: Move all the x terms to one side. Add $2x$ to both sides:

$18x + 2x - 81 > 0$

$20x - 81 > 0$

Step 4: Isolate x. Add $81$ to both sides:

$20x > 81$

Step 5: Solve for x. Finally, divide both sides by $20$ to get the value of x:

$x > \frac{81}{20}$

So the solution to the inequality is $x > \frac{81}{20}$ or $x \in \left(\frac{81}{20}, +\infty\right)$.