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Which statement about sqrt x-5 minus sqrt x=5 true?

-3 is a true solution

-3 is a extraneous solution

9 is a true solution

9 is a extraneous solution

User Heyitsjhu
by
8.3k points

2 Answers

6 votes

Answer:

D.) x = 9 is an extraneous solution.

Explanation:

User A Spoty Spot
by
8.3k points
1 vote

Answer:

9 is an extraneous solution.

Explanation:

Extraneous solution is a solution that when plugged into the equation do not hold true.

Here we are given an algebraic equation in terms of single variable x as:


√(x-5)-√(x)=5-----(1)

Now, we will solve this equation to obtain the solution as:

on squaring both side of the equation we obtain:


(√(x-5)-√(x))^2=5^2


x-5+x-2√(x-5)√(x)=25\\\\2x-5-2√(x-5)√(x)=25\\\\2x-30=2√(x-5)√(x)\\\\on\ dividing\ both\ side\ by\ 2\ we\ obtain:\\\\x-15=√(x-5)√(x)

Again on squaring both side of the equation we obtain:


x^2+225-30x=(x-5)x\\\\\x^2+225-30x=x^2-5x\\\\225=-5x+30x\\\\225=25x\\\\x=9

Now when we plug x=9 back to the original equation i.e. equation (1) we get:


√(9-5)-√(9)=5\\\\√(4)-√(9)=5\\\\2-3=5\\\\-1=5

Hence, the equation does not hold true.

Hence, 9 is a extraneous solution

User Crobicha
by
8.5k points

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