## JozelynW one year ago Create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. Use the equation below as a model.

1. JozelynW

How to make a extraneous solution?

2. JozelynW

@ikram002p

3. JozelynW

@welshfella

4. JozelynW

do you know how to write a extraneous radical equation

5. xapproachesinfinity

extraneous sol is solution that is not in the domain of the equation you started with

6. JozelynW

huh

7. JozelynW

well, then how do I create a radical extraneous equation?

8. xapproachesinfinity

consider the following equation $$\sqrt{\frac{x+1}{x}}=\sqrt{\frac{1}{x}}$$ see that x=0 is not in the domain try to solve that equation

9. xapproachesinfinity

it is easier to create an equation with correct solution (not extraneous )

10. welshfella

-3 sqrt(7 + 2x) = 24 sqrt(7 + 2x) = -8 square both sides 7 + 2x = 64 2x = 57 x = 57/2 now plug in x = 57/2 and see if it satisfies the original equation

11. xapproachesinfinity

consider the following equation $$\sqrt{x+1}=\sqrt{3x-1}$$ solution is $$x=1$$ if we check it on the equation we it checks out

12. JozelynW

it wants me to use this equation a√x+b+c=d

13. xapproachesinfinity

you just said radical equation you did specify any details

14. xapproachesinfinity

well at any rate check @welshfella work

15. JozelynW

I know because then you would just be giving me answers and then people would be thinking that im cheating

16. welshfella

a negative number times a radical will give an extraneous solution

17. JozelynW

so i just wanted to know how to create a radical extraneous equation

18. JozelynW

can you give me an example

19. welshfella

if you plug in 57/2 into the above it won't give you 24

20. JozelynW

but it's suppose to

21. JozelynW

28.5

22. welshfella

no - ones like that will give an extraneous solution When you square you get a positive result so a negative value can get 'lost'.

23. JozelynW

so 28.5 is not 57/2

24. welshfella

-3 * sqrt(7 + 28.5) = -17.87

25. JozelynW

what do you mean sqrt ? sqrt of 3

26. welshfella

do you see that this is an extraneous solution?

27. welshfella

square root of (7 + 28.5)

28. JozelynW

i do it equals -17.87

29. JozelynW

wait did something wrong

30. JozelynW

sqrt of 35.5 =5.95 and 5.95 times -3 equals -17.87

31. welshfella

yes that is correct so 28.5 is not a solution its extraneous

32. welshfella

now one that does not have an extraneous solution would be sqrt(4x + 1) = 7 so 4x + 1 = 49 4x = 48 x = 12 which will fit the original equation

33. welshfella

34. JozelynW

what are the options

35. welshfella

what do you mean?

36. JozelynW

you said " which will fit the original equation"

37. welshfella

I meant if you replace x by 12 in the original equation then the equation will balance the left side will equal 7

38. welshfella

sqrt(4*12 + 1) = sqrt 49 = 7

39. welshfella

so x = 12 is a valid solution

40. JozelynW

so the rule to this is.......

41. welshfella

a negative value as above will give an extraneous solution. But there' more to it than that that's why i posted the link. Some equations will have one valid and one extraneous solution , for example.

42. welshfella

sorry but i have to go now

43. JozelynW

thank you so much for you help @welshfella

44. welshfella

yw