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`sqrt(9y - 196) + sqrt196= sqrt49` Solve for y.

loishy's profile pic

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`sqrt(9y - 196) + sqrt196= sqrt49`

Solve for y.

5 Answers | Add Yours

pramodpandey's profile pic

Posted (Answer #13)

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`sqrt(x^2)=+-x`

To mention this in this problem is not  correct

When we have specially given plus sign only.

The solutions of the equation are  `245/9` and `637/9`  given by one educator.Let verify its validty in given equation (fortunately you can not change equation)

`sqrt(9y-196)+sqrt(196)=sqrt(49)`

`y=245/9`

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

`sqrt(245-196)+sqrt(196)=sqrt(49)`

`sqrt(49)+sqrt(196)=sqrt(49)`

Is it correct ? Now How will you justify  answer ! No.

`y=637/9`

`sqrt(9xx(637/9)-196)+sqrt(196)=sqrt(49)`

`sqrt(637-196)+sqrt(196)=sqrt(49)`

`sqrt(441)+sqrt(196)=sqrt(49)`

Is is correct  ? Again can you justify answer ! Never

This equation has no real root at all . If talk about complex root then it may possible.

`sqrt(9y-196)+sqrt(196)=sqrt(49)`

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

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

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

`9y=196+49i^4`

`9y=245`

`y=245/9`

But we have shown above `y=245/9`  does not satisfy the given equation.

Thus this equation has neither real root nor complex root.

So logic is simple

Nonnegative real number never equal to negative number.

oldnick's profile pic

Posted (Answer #3)

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`sqrt(9y-196)+sqrt(196)=sqrt(49)`

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

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

`sqrt(9y-196)= +-21`  `sqrt(9y-196)=+-7`

`9y-196=441`     `9y-196= 49`

`9y= 637`               `9y= 245`

`y=637/9`                    `y=245/9`

Proof:

`y=637/9`

`sqrt(637-196)+sqrt(196)=sqrt(49)`

`sqrt(441)+sqrt(196)=sqrt(49)`

`+-21+-14=+-7`

That is:

`21-14=7`   and   `-21+14=-7`

proof `637/9`   OK.

Proof `245/9` :

`sqrt(245-196)+sqrt(196)=sqrt(49)`

`sqrt(49)+sqrt(196)=sqrt(49)`

`+-7+-14=+-7`

That is :

`-7+14=7`          `7-14=-7`

proof `245/9`   OK.

 

 

 

pramodpandey's profile pic

Posted (Answer #7)

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We  have given

`sqrt(9y-196)=sqrt(49)-sqrt(196)`

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

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

which is not possible , because left hand side is positive and right hand side is negative.

Thus  this equation has no root.

mariloucortez's profile pic

Posted (Answer #11)

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You have `sqrt(9y - 196) + sqrt(196) = sqrt(49)`

Fisrt simplify first the terms that can be simplified like `sqrt(196)` and `sqrt(49)`

They are perfect square.

`sqrt(196) = 14` 

`sqrt(49)=7`

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

Simplify further by combining similar terms. Move 14 to the right side, thus changing the sign to negative. Remeber that moving a term to the other side will change the sign.

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

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

 

Take the square of both sides to get rid of the radical or square root.

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

`9y - 196 = 49`

Combine similar terms.

`9y = 49 +196`    

`9y = 245`

Divide both sides by the number beside y to leave y alone at the left side.

`(9y)/9 = 245/9`

 `y = 27.22222`

`` or you can just leave `245/9` alone.

Check your answer by substituting 245/9 into y in the original given.

`sqrt(9*245/9) + sqrt(196) = sqrt(49)`

Simplifying that using your calculator, you have 29.65248 on the left side while you have 7 at the right side.

You can conclude that the right side and the left side of the equation are not equal so therefore what you get for y is not a solution of the equation.

justaguide's profile pic

Posted (Answer #12)

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The equation `sqrt(9y - 196) + sqrt 196 = sqrt 49` has to be solved for y.

`sqrt(9y - 196) + sqrt 196 = sqrt 49`

=> `sqrt(9y - 196) = sqrt 49 - sqrt 196`

 `sqrt 49 = +- 7` and `sqrt 196 = +-14`

This gives:

`sqrt (9y - 196) = 21`

=> `9y - 196 = 441`

=> `y = 637/9`

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

=> `9y - 196 = 49`

=> `y = 245/9`

`sqrt(9y - 196) = 7`

=> `y = 245/9`

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

=> `y = 637/9`

The solutions of the equation are `245/9` and `637/9`

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