Sqrt (6m + 7) - sqrt (3m + 3) = 1 #Solve the radical equations, if possible

Question

Sqrt (6m + 7) - sqrt (3m + 3) = 1 #Solve the radical equations, if possible 

Answer 1

Lauren, you need to learn how to do these on your own.  This is a similar problem that I answered for you earlier.

Answer 2

√(6m+7) - √(3m+3) = 1

 

add √(3m+3) to both sides

 

√(6m+7) = 1 + √(3m+3)

 

square both sides

 

6m+7 = 1 + 2√(3m+3) + 3m + 3

 

6m + 7 = 2√(3m+3) + 3m + 4

 

subtract (3m+4) from both sides

 

3m + 3 = 2√(3m+3)

 

square both sides

 

9m² + 18m + 9 = 4(3m+3)

9m² + 18m + 9 = 12m + 12

 

subtract (12m+12) from both sides

 

9m² + 6m -3 = 0

Factor out a 3 from each term

3(3m² + 2m - 1) = 0

3m² + 2m - 1 = 0

 

We can factor by grouping

3(-1) = -3

Factors of -3 that add to 2 are 3(-1)

Replace 2m with 3m - m in the polynomial

 

3m² + 3m - m -1 = 0

 

3m(m+1) - (m+1) = 0

(3m-1)(m+1) = 0

 

either 3m-1 = 0    OR   m+1 = 0

         3m = 1               m = -1

          m = 1/3

 

We have two solutions:  m = -1, 1/3

 

Plugging these into the original problem we see that

both actually do work.