(х2-25) 2+(х2+2х-15) 2=0

Question 1

Задача Задача №29755

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Аноним

31 октября 2023 08:59 · публичный вопрос

А

Аноним 31 октября 2023 08:59

(х2-25) 2+(х2+2х-15) 2=0

Answer

To solve the equation (x^2 - 25)^2 + (x^2 + 2x - 15)^2 = 0, we can expand the equation and simplify.

Expanding the first term (x^2 - 25)^2: (x^2 - 25)^2 = (x^2 - 25)(x^2 - 25) = x^2(x^2) + x^2(-25) - 25(x^2) - 25(-25) = x^4 - 50x^2 + 625

Expanding the second term (x^2 + 2x - 15)^2: (x^2 + 2x - 15)^2 = (x^2 + 2x - 15)(x^2 + 2x - 15) = x^2(x^2) + x^2(2x) - x^2(15) + 2x(x^2) + 2x(2x) - 2x(15) - 15(x^2) - 15(2x) + 15(15) = x^4 + 2x^3 - 15x^2 +2x^3 + 4x^2 - 30x - 15x^2 - 30x + 225 = x^4 + 4x^3 - 26x^2 - 60x + 225

Now, substituting these expanded forms into the original equation: (x^4 - 50x^2 + 625) + (x^4 + 4x^3 - 26x^2 - 60x + 225) = 0

Combining like terms: 2x^4 + 4x^3 - 76x^2 - 60x + 850 = 0

Unfortunately, this equation cannot be factored further. To find the solution, numerical methods or graphing techniques may be necessary.

Question 2

(х2-25) 2+(х2+2х-15) 2=0

Answer

To solve the equation (x^2 - 25)^2 + (x^2 + 2x - 15)^2 = 0, we can expand the equation and simplify. Expanding the first term (x^2 - 25)^2: (x^2 - 25)^2 = (x^2 - 25)(x^2 - 25) = x^2(x^2) + x^2(-25) - 25(x^2) - 25(-25) = x^4 - 50x^2 + 625 Expanding the second term (x^2 + 2x - 15)^2: (x^2 + 2x - 15)^2 = (x^2 + 2x - 15)(x^2 + 2x - 15) = x^2(x^2) + x^2(2x) - x^2(15) + 2x(x^2) + 2x(2x) - 2x(15) - 15(x^2) - 15(2x) + 15(15) = x^4 + 2x^3 - 15x^2 +2x^3 + 4x^2 - 30x - 15x^2 - 30x + 225 = x^4 + 4x^3 - 26x^2 - 60x + 225 Now, substituting these expanded forms into the original equation: (x^4 - 50x^2 + 625) + (x^4 + 4x^3 - 26x^2 - 60x + 225) = 0 Combining like terms: 2x^4 + 4x^3 - 76x^2 - 60x + 850 = 0 Unfortunately, this equation cannot be factored further. To find the solution, numerical methods or graphing techniques may be necessary.