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Find the number if the square root of another number that is 6 greater than this number is equal to the number itself.

User Spacetyper
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1 Answer

3 votes

Answer:

3

Explanation:

Let x represent the number of interest. Then x+6 is "another number". You want its square root to be the original number:

√(x+6) = x

Squaring both sides, we get ...

x +6 = x^2

In standard form, this is ...

x^2 -x -6 = 0

(x -3)(x +2) = 0 . . . . factored

By the zero product rule, this will have solutions ...

x -3 = 0 ⇒ x = 3

x +2 = 0 ⇒ x = -2 . . . . . an extraneous solution, because √(-2+6) ≠ -2

The number is 3.

User Anthony Tietjen
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