Question

|x^2-25|+|x^2-1|=24​

Answer 1

Ответ:

x€ [-5 , -1] ¥ [1 , 5]

Объяснение:

там дуже багато писати....

Answer 2

To solve the equation |x^2 - 25| + |x^2 - 1| = 24, we can consider different cases based on the values of x.

Case 1: x^2 - 25 ≥ 0 and x^2 - 1 ≥ 0 In this case, both absolute values are positive, so we can remove the absolute value signs without changing the equation.

x^2 - 25 + x^2 - 1 = 24 2x^2 - 26 = 24 2x^2 = 50 x^2 = 25 x = ±5

Case 2: x^2 - 25 < 0 and x^2 - 1 ≥ 0 In this case, the first absolute value is negative, so we need to take its negation when removing the absolute value sign.

-(x^2 - 25) + (x^2 - 1) = 24

• x^2 + 25 + x^2 - 1 = 24 24 + 24 = 50 --> False

Case 3: x^2 - 25 ≥ 0 and x^2 - 1 < 0 In this case, the second absolute value is negative, so we need to take its negation when removing the absolute value sign.

(x^2 - 25) + -(x^2 - 1) = 24 x^2 - 25 - x^2 + 1 = 24 -24 + 1 = 24 --> False

Case 4: x^2 - 25 < 0 and x^2 - 1 < 0 In this case, both absolute values are negative, so we need to take the negation of both expressions when removing the absolute value signs.

-(x^2 - 25) + -(x^2 - 1) = 24

• x^2 + 25 - x^2 + 1 = 24 26 = 24 --> False

Therefore, the only solution that satisfies the equation is x = ±5.