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Square roots

By convention x^{1/2} means the principle root of x i.e. the positive one.
but then why does x^2-9=0 have two roots 3 and -3?

Reply 1

username1732133

Original post by runny4

By convention x^{1/2} means the principle root of x i.e. the positive one.
but then why does x^2-9=0 have two roots 3 and -3?

See here: http://www.thestudentroom.co.uk/showthread.php?t=3173187

Reply 2

phoenixsilver

Because expanding (x+3)(x-3) gives x^2-9

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Reply 3

davros

Original post by runny4

By convention x^{1/2} means the principle root of x i.e. the positive one.
but then why does x^2-9=0 have two roots 3 and -3?

I'm not sure what your problem is!

As you say, x^(1/2) denotes the positive square root when x is a positive real number.

The equation x^2 - 9 = 0 has two distinct solutions, +3 and -3, and these are referred to as the roots of the equation.

There's no inconsistency or confusion here :smile: