Question

| х ² - 4 | - | 9 - х ²| = 4

Answer 1

x²-4-9+x²=4

2x²=17

x²=17/2=8,5

x=√8,5 x=-√8,5

-x²+4+9-x²=4

-2x²=-9

x²=4.5

x=√4.5 x=-√4.5

Answer 2

The equation you've provided is a bit challenging to solve algebraically due to the absolute value terms. To solve it, we'll need to consider different cases based on the sign of the expressions inside the absolute value bars.

Let's break it down step by step:

|х² - 4| - |9 - х²| = 4

Case 1: х² - 4 is positive (х² - 4 ≥ 0) In this case, the first absolute value simplifies to х² - 4, and the second absolute value simplifies to 9 - х². So, the equation becomes:

х² - 4 - (9 - х²) = 4

Simplify and solve for x:

2х² - 13 = 4 2х² = 17 х² = 17/2

However, this doesn't lead to a real solution, since the square root of 17/2 is not a real number.

Case 2: х² - 4 is negative (х² - 4 < 0) In this case, the first absolute value simplifies to -(х² - 4), and the second absolute value simplifies to 9 - х². So, the equation becomes:

-(х² - 4) - (9 - х²) = 4

Simplify and solve for x:

-2х² + 13 = 4 -2х² = -9 х² = 9/2

Again, this doesn't lead to a real solution.

Since both cases lead to solutions that are not real numbers, it seems that there are no real solutions to the given equation.

Please double-check the equation or provide additional context if there might be an error or if you have specific constraints on the values of x.