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tahayassen
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[tex]±\sqrt { { x }^{ 2 } } \\ =±|x|\\ =±±x[/tex]
Wouldn't a plus sign or a minus sign be sufficient?
Wouldn't a plus sign or a minus sign be sufficient?
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tahayassen said:Wouldn't a plus sign or a minus sign be sufficient?
plus/minus signs
This last step is incorrect. [itex]\pm\sqrt{x^2}[/itex] is the same as [itex]\pm |x|[/itex] but |x| is NOT the same as "[itex]\pm x[/itex]" so [itex]\pm |x|[/itex] is NOT the same as "[itex]\pm\pm x[/itex]".tahayassen said:[tex]±\sqrt { { x }^{ 2 } } \\ =±|x|\\ =±±x[/tex]
How would you chose which?Wouldn't a plus sign or a minus sign be sufficient?
The plus/minus sign in front of a radical indicates that there are two possible solutions for the equation. This is because a radical represents the square root of a number, and both the positive and negative square root of a number are valid solutions.
No, using only the positive sign in front of radicals would restrict the solutions to only positive values, and there are cases where negative values are also valid solutions. The plus/minus sign allows for both positive and negative solutions to be considered.
We use the plus/minus sign in front of radicals when solving equations that involve finding the square root of a variable. This is because the variable could have both a positive and negative value as its square root, so the plus/minus sign allows us to consider both possibilities.
Yes, the plus/minus sign can also be used with other types of radicals, such as cube roots or higher order roots. This is because the concept of having both a positive and negative solution still applies.
No, there is no specific order for using the plus/minus sign with other mathematical operations. It is typically used after other operations, such as addition or subtraction, have been performed on the equation.