Question

Д)(y+1)^2/12-1-y^2/24=4

Answer 1

I hope this helps you

Answer 2

To solve the equation (y+1)^2/12 - 1 - y^2/24 = 4, we can follow these steps:

Step 1: Multiply through by the common denominator of 12 and 24 to eliminate the fractions: 24 * [(y+1)^2/12] - 24 * (1) - 12 * [y^2/24] = 4 * 24

This simplifies to: 2 * (y+1)^2 - 24 - y^2 = 96

Step 2: Expand and simplify the equation: 2 * (y^2 + 2y + 1) - 24 - y^2 = 96 2y^2 + 4y + 2 - 24 - y^2 = 96 y^2 + 4y - 118 = 0

Step 3: Rearrange the equation into standard quadratic form: y^2 + 4y - 118 = 0

Step 4: Solve the quadratic equation using factoring, completing the square, or the quadratic formula. In this case, the quadratic equation does not factor nicely, so we'll use the quadratic formula:

y = (-b ± √(b^2 - 4ac)) / (2a)

For the equation y^2 + 4y - 118 = 0, a = 1, b = 4, and c = -118. Plugging these values into the quadratic formula:

y = (-4 ± √(4^2 - 4 * 1 * -118)) / (2 * 1) y = (-4 ± √(16 + 472)) / 2 y = (-4 ± √488) / 2 y = (-4 ± 22.1) / 2

So, the solutions for y are: y = (-4 + 22.1) / 2 ≈ 9.05 y = (-4 - 22.1) / 2 ≈ -13.05

Therefore, the solutions to the equation (y+1)^2/12 - 1 - y^2/24 = 4 are approximately y = 9.05 and y = -13.05.