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heres a problem i stumbled:
find three rational numbers a,b,x such that:
x^2 + 5 = a^2
x^2 - 5 = b^2
find three rational numbers a,b,x such that:
x^2 + 5 = a^2
x^2 - 5 = b^2
Let's assume that [itex]a,b[itex] and [itex]x[/itex] are integers.dextercioby said:Can u find the integer ones...?
To find rational numbers satisfying a quadratic equation, you can use the quadratic formula or factor the equation and solve for the roots.
The quadratic formula is a mathematical formula used to solve quadratic equations, which are equations in the form of ax^2 + bx + c = 0. The formula is x = (-b ± √(b^2 - 4ac)) / 2a.
Yes, a quadratic equation can have irrational solutions. For example, the equation x^2 - 2 = 0 has the solutions x = ±√2, which are irrational numbers.
A quadratic equation can have a maximum of two rational solutions. However, it is also possible for a quadratic equation to have no rational solutions or one repeated rational solution.
Rational numbers are numbers that can be expressed as a ratio of two integers, while irrational numbers cannot be expressed as a ratio of two integers. Irrational numbers are often decimal numbers that do not terminate or repeat, such as √2 or π.