Question

Y^2= -8x+16, 2x-y=0

Answer 1

Ответ:

y=x^2 - 8x + 16

2x - 3y = 0

y=x^2 - 8x + 16

2x-3(x^2 - 8x + 16)=0

y=x^2 - 8x + 16

3x^2-26x+48=0⇒x=8/3 и x=6

x=8/3

y=(8/3)^2-8*8/3+16=16/9

x=6

y=36-8*6+16=4

Пошаговое объяснение:

Answer 2

To find the point of intersection between the two equations:

1. Start with the equation 2x - y = 0.
2. Solve this equation for y to express y in terms of x: 2x - y = 0 -y = -2x y = 2x

Now you have y expressed in terms of x.

3. Substitute this expression for y into the equation y^2 = -8x + 16: (2x)^2 = -8x + 16

4. Simplify the equation: 4x^2 = -8x + 16

5. Move all terms to one side to set the equation equal to zero: 4x^2 + 8x - 16 = 0

6. Divide the entire equation by 4 to simplify it further: x^2 + 2x - 4 = 0

7. Now, you have a quadratic equation. You can solve it using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = 2, and c = -4. Plug these values into the formula:

x = (-2 ± √(2² - 4(1)(-4))) / (2(1)) x = (-2 ± √(4 + 16)) / 2 x = (-2 ± √20) / 2 x = (-2 ± 2√5) / 2 x = -1 ± √5

Now you have two possible x-values: x₁ = -1 + √5 and x₂ = -1 - √5.

8. Use the expression y = 2x to find the corresponding y-values for these x-values: For x₁ = -1 + √5: y₁ = 2(-1 + √5) = -2 + 2√5

   For x₂ = -1 - √5: y₂ = 2(-1 - √5) = -2 - 2√5

So, the points of intersection are (-1 + √5, -2 + 2√5) and (-1 - √5, -2 - 2√5).