## anonymous 5 years ago Hi I need to find the solution set for the following equation √(10x+5) - √(6x-11) =6

1. anonymous

you sure that is a "-" and not a "+"?

2. anonymous

Yes the equation is correct

3. anonymous

too bad because if it was a +, 2 would work by inspection. this problem is a pain. you have to square twice

4. anonymous

And it says solve the equation. The solution set is blank and blank

5. anonymous

ok let me work it out. i was trying to guess what would give a perfect square for 10x+5 and 6x-11

6. anonymous

Thx

7. anonymous

2 works because 2*10+5=25 and 6*2-11=1

8. anonymous

and 5+1=6

9. anonymous

So would the sol set be 5,1

10. anonymous

no the solution would be x = 2, but it is not. i am still working.

11. anonymous

have to square both sides, then square again. i will show you but i want to get a correct answer so i don't blow it.

12. anonymous

good heavens. i will be back in ten minutes with the answer and the algebra. hold on.

13. anonymous

K :-)

14. anonymous

62

15. anonymous

16. anonymous

would you like a worked out solution?

17. anonymous

square both sided. you will get $16x-6-2\sqrt{(10x+5)(6x-11)}=36$

18. anonymous

$-2\sqrt{(10x+5)(6x-11)}=42-16x$

19. anonymous

divide by -2 $\sqrt{(10x+5)(6x-11)}=8x-21$

20. anonymous

so is there only one solution of 62

21. anonymous

sorry my computer is slow

22. anonymous

then square again. you will get $(10x-5)(6x-11)=(8x+21)^2$

23. anonymous

yes only one answer. you will solve a quadratic and get two solutions but only one will work.

24. anonymous

introduced a false solution when you squared

25. anonymous

typo on last answer. it should have been $(10x+5)(6x-11)=(8x-21)^2$

26. anonymous

thx u

27. anonymous

expand these to get $60x^2-80x-55=64x^2-336x+441$

28. anonymous

set =0 and solve: $4x^2-256x+496=0$ divide by 4 $x^2-64x+124=0$

29. anonymous

factor $(x-62)(x-2)=0$ $x=62$ or $x=2$

30. anonymous

but there is only one answer because 2 does not work. if you replace x by 2 in the original equation you get $\sqrt{25}-\sqrt{1}=6$ $5-1=6$ which is false.

31. anonymous

negatives on both?? thx

32. anonymous

62 will work but only 62, not 2.

33. anonymous

oh negatives on both when factoring. but the only answer is x = 62

34. anonymous

you have to plug it into the original equation

35. anonymous

$\sqrt{10\times 62+5}-\sqrt{6\times 62-11}$ $\sqrt{625}-\sqrt{361}=25-19=6$

36. anonymous

i am confused i just need the solution set

37. anonymous

solution is 62

38. anonymous

62 works, 2 does not

39. anonymous

ok...thx