Math Is Fun Forum

Daddio

Member

Registered: 2008-11-25

Posts: 1

Adding Sqr Roots with exponents in them

Can anyone help me understand how to solve this problem???  Thanks for the help.
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√2x-1 + √x+3  = 3

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Adding Sqr Roots with exponents in them

I can't think how you'd solve a general problem like that, but this one is doable.

Both of the terms on the left are strictly increasing (making x bigger always makes them bigger), and so there can only be one value of x that fits.

That one value is fairly easy to find by guessing.

Edit: Ah, luca's done it properly. Squaring both sides still leaves a square root, but I didn't think to square again.

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luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Adding Sqr Roots with exponents in them

trying both values in original equation shows that x = 1 is a solution, and x = 61 is invalid.

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TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: Adding Sqr Roots with exponents in them

Actually, x = 61 is valid.  The original problem doesn't restrict us to positive square roots, so you get 11 + (-8) = 3.

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Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Adding Sqr Roots with exponents in them

When square roots appear without a ±, this typically means you only take the positive root.  Otherwise, just having the symbol "±" along with a square root would be redundant.

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