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A level Maths

What is the rule for plus minus sign?Should we put +-sign when square or square root both side?Is it applicable for fourth root also?
Reply 1
in algebra generally no, if you were to square root x^2 you would generally just write x by convention, but if you have a quadratic such as x^2=4, then when square rooting it is nescessary to specify that the root is plus or minus 2
Original post by DanLR
in algebra generally no, if you were to square root x^2 you would generally just write x by convention, but if you have a quadratic such as x^2=4, then when square rooting it is nescessary to specify that the root is plus or minus 2


If it's x^4=1, should we put +-
Reply 3
Original post by Sasha Shasha
If it's x^4=1, should we put +-


You need to be careful because that equation has 2 real roots and 2 imaginary roots (if you've covered complex numbers).

The real solutions are given by x=±1x = \pm 1.

But note that 14=1\sqrt[4]{1} = 1 because a function must be defined to return a single value :smile:
Original post by davros2
You need to be careful because that equation has 2 real roots and 2 imaginary roots (if you've covered complex numbers).

The real solutions are given by x=±1x = \pm 1.

But note that 14=1\sqrt[4]{1} = 1 because a function must be defined to return a single value :smile:


I still don't understand:frown:
Reply 5
Original post by Sasha Shasha
I still don't understand:frown:


What don't you understand? Equations like x^2 = 1 and x^4 = 1 have 2 and 4 solutions respectively (or 2 and 2 if you're restricted to real numbers only), so when you're listing the solutions you can cover them in pairs by using the plus/minus symbol, but functions have to be 1-1 or many-1, so you can only write 1=1\sqrt{1} = 1 - it is incorrect to write 1=±1\sqrt{1} = \pm 1

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