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How many real solutions (intersectio) will there be in the system of two equations

How many real solutions (intersectio) will there be in the system of two equations-example-1
User Romatthe
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Answer:

  • No real solutions

==============

Given is the system of equations.

Solve it by substitution, y = 8x²:

  • x² - y² = 1
  • x² - (8x²)² = 1
  • x² - 64x⁴ = 1
  • 64x⁴ - x² + 1 = 0

Find the discriminant of the quadratic equation, if it is positive there are two real solutions, if zero then one solution, if negative then no solution.

  • D = (-1)² - 4*64*1
  • D = -255

Since D < 0 there are no real solutions (intersections).

User Sgryzko
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