Question

The equation x2 = d has how many real solutions when d > 0?

Answer 1

Two:
`√(d)` and
`\left(-√(d)\right)`.

Explanation:

The question is asking for the number of real numbers
`x` whose square is equal to
`d` (where
`d > 0`.)

Naturally, the square root of
`d`:
`√(d)` would satisfy the requirement.
`\left(√(d)\right)^(2) = d`.

However, keep in mind that
`(x)^2` and
`(-x)^(2)` have the same value. Therefore, if
`x =√(d)` would satisfy the equation, the opposite
`x = -√(d)` would also do.

Since
`d > 0`,
`√(d)` and
`\left(-√(d)\right)` would both take real values.

Because
`d \\e 0`, the value of
`√(d)` and
`\left(-√(d)\right)` would be distinct.

Hence,
`√(d)` and
`\left(-√(d)\right)` would correspond to the two real solutions of this equation.