`sqrt(9y-196)`  + `sqrt(196)` = `sqrt(49)`    Simplify. I do not think there are any solutions, is that right? Thanks in advance :)

Expert Answers
jgeertz eNotes educator| Certified Educator

You are absolutely correct. There are no solutions. Let's solve the problem to see why.

`sqrt(9y-196) +sqrt(196) = sqrt49`

Remove all the perfect squares from under the radical. In this problem both 7 and 14 are perfect squares.

`sqrt(9y-196) +14=7`

Subtract 14 from both sides of the equation.

`sqrt(9y-196) =-7`

Now to eliminate the radical on the left side of the equation, square both sides of the equation.

`(sqrt(9y-196))^2 =(-7)^2`

Simplify.

`9y-196 =49`

Add 196 to both sides of the equation.

`9y=245`

Divide both sides by 9 and simplify.

`y= 245/9`

In order to be a valid solution, it must work when substituted into the original equation.

`sqrt(9(245/9)-196) +sqrt196 =sqrt49`

`sqrt(245-196) + 14 =7`

`sqrt49 +14=7`

`7+14=7`

21 not equal to 7

Therefore the problem has no solution.

 

oldnick | Student

you have more  equation in one:

 

`sqrt(9y-196)+-14=+-7`

`sqrt(9y-196)=+-7+-14`

`sqrt(9y-196)=+-21`           (1)

`sqrt(9y-196)=+-7`                (2)

  Solving:  (1)

`sqrt(9y-196)= +- 21`

`9y-196=441`

`9y=637`       `rArr y=637/9`

Solving (2):

`sqrt(9y-196)=+-7`

`9y-196=49`

`9y= 215`       `rArr y=245/9`

Indeed:

`sqrt(9xx637/9-196)=sqrt(637-196)=sqrt(441)=+-21` 

 `sqrt(9xx 245/9-196)=` `sqrt(245-196)=sqrt(49)=+-7`

 

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