How can 2x² = x² + 4x + 8 be set up as a system of equations?

Solution:

Let y = 2x² --------------- (1)

y = x² + 4x + 8 --------------- (2)

By substituting the value of y in equation 2, we get

⇒ 2x² = x² + 4x + 8

⇒ 2x² - x² - 4x - 8 = 0

⇒ x² - 4x = 8

By solving the equation using completing the square method, add 2² to both sides of the above equation. We have

⇒ x² - 4x + (2)² = 8 + (2)²

⇒  (x - 2)² = 8 + 4

By square root on both the sides we get

⇒ x - 2 = ± √12

⇒  x = 2 ± 2√3

From this we get two values of x

x = 2 + 2√3 or 2 - 2√3

The system of equations will have the same solutions for x.

Therefore, the system of quadratic equations can be set up as y = 2x², y = x² + 4x + 8 and its solution is x = 2 + 2√3 or x = 2 - 2√3.

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How can 2x² = x² + 4x + 8 be set up as a system of equations?

Summary:

2x² = x² + 4x + 8 can be set up as a system of equations as y = 2x², y = x² + 4x + 8 and its solution is x = 2 + 2√3 or x = 2 - 2√3.