Question

Which statement describes a process to solve _/b+20 - _/D=5?

Add a radical term to both sides and square both sides only once.
O Add a constant term to both sides and square both sides only once.
O Add a radical term to both sides and square both sides twice.
O Add a constant term to both sides and square both sides twice.

Answer 1

d

Explanation:

double check your answer

Answer 2

C. Add a radical term to both sides and square both sides twice

Explanation:

We suppose you want to solve ...

`√(b+20)-√(d)=5\\\\√(b+20)=5+√(d)\qquad\text{add a radical term}\\\\b+20=25+10√(d)+d\qquad\text{square both sides once}\\\\b-d-5=10√(d)\qquad\text{subtract right-side non-radical terms}\\\\(b-d-5)^2=100d\qquad\text{square both sides a second time}`

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We note that the solution summary (choice C) doesn't mention the fact that you need to separate the remaining radical term from the others after the first squaring.

The result is a quadratic function that produces extraneous solutions. This is shown in the attached graph. The red function is the original relation between b (x) and d (y). The blue function includes the red function and another branch that is all extraneous solutions.