Question

Решите уравнение.

Answer 1

Переносим всё в левую часть:
y^4 + 2y^2 - 10y^2 + 16 = 0
Приводим подобные:
y^4 - 8y^2 + 16 = 0
Делаем замену t = y^2:
t^2 - 8t + 16 = 0
Решаем обычное квадратное уравнение: корень один t = 4

       8 ± √(8^2 - 4*16)
t = ------------------------- = 4
             2*1

Возвращаемся к исходной переменной:
y^2 = t = 4; отсюда y = ±2

Проверка:
2*(±2)^2 +16 = 8+ 16 = 24
10* (±2)^2 - (±2)^4 = 40 - 16 = 24
Всё верно.

Answer 2

Делаем замену:
y^2=x
получим:
2x+16=10x-x^2
x^2-8x+16=0
x^2-2*4*x+4^2=0
(x-4)^2=0
x-4=0
x=4
y^2=4 y1=2 y2=-2 Ответ: y1=2; y2=-2

Answer 3

Solving the Equation

To solve the equation x3,5+x=180, we need to isolate the variable x on one side of the equation. Here's how we can do it:

1. Subtract 3.5 from both sides of the equation: x + 3.5 = 180 - 3.5

2. Simplify the right side of the equation: x + 3.5 = 176.5

3. Subtract 3.5 from both sides of the equation to isolate x: x = 176.5 - 3.5

4. Simplify the right side of the equation: x = 173

Therefore, the solution to the equation x3,5+x=180 is x = 173.