anonymous
  • anonymous
Hi I need to find the solution set for the following equation √(10x+5) - √(6x-11) =6
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
you sure that is a "-" and not a "+"?
anonymous
  • anonymous
Yes the equation is correct
anonymous
  • anonymous
too bad because if it was a +, 2 would work by inspection. this problem is a pain. you have to square twice

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anonymous
  • anonymous
And it says solve the equation. The solution set is blank and blank
anonymous
  • anonymous
ok let me work it out. i was trying to guess what would give a perfect square for 10x+5 and 6x-11
anonymous
  • anonymous
Thx
anonymous
  • anonymous
2 works because 2*10+5=25 and 6*2-11=1
anonymous
  • anonymous
and 5+1=6
anonymous
  • anonymous
So would the sol set be 5,1
anonymous
  • anonymous
no the solution would be x = 2, but it is not. i am still working.
anonymous
  • 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.
anonymous
  • anonymous
good heavens. i will be back in ten minutes with the answer and the algebra. hold on.
anonymous
  • anonymous
K :-)
anonymous
  • anonymous
62
anonymous
  • anonymous
is the answer
anonymous
  • anonymous
would you like a worked out solution?
anonymous
  • anonymous
square both sided. you will get \[16x-6-2\sqrt{(10x+5)(6x-11)}=36\]
anonymous
  • anonymous
\[-2\sqrt{(10x+5)(6x-11)}=42-16x\]
anonymous
  • anonymous
divide by -2 \[\sqrt{(10x+5)(6x-11)}=8x-21\]
anonymous
  • anonymous
so is there only one solution of 62
anonymous
  • anonymous
sorry my computer is slow
anonymous
  • anonymous
then square again. you will get \[(10x-5)(6x-11)=(8x+21)^2\]
anonymous
  • anonymous
yes only one answer. you will solve a quadratic and get two solutions but only one will work.
anonymous
  • anonymous
introduced a false solution when you squared
anonymous
  • anonymous
typo on last answer. it should have been \[(10x+5)(6x-11)=(8x-21)^2\]
anonymous
  • anonymous
thx u
anonymous
  • anonymous
expand these to get \[60x^2-80x-55=64x^2-336x+441\]
anonymous
  • anonymous
set =0 and solve: \[4x^2-256x+496=0\] divide by 4 \[x^2-64x+124=0\]
anonymous
  • anonymous
factor \[(x-62)(x-2)=0\] \[x=62\] or \[x=2\]
anonymous
  • 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.
anonymous
  • anonymous
negatives on both?? thx
anonymous
  • anonymous
62 will work but only 62, not 2.
anonymous
  • anonymous
oh negatives on both when factoring. but the only answer is x = 62
anonymous
  • anonymous
you have to plug it into the original equation
anonymous
  • anonymous
\[\sqrt{10\times 62+5}-\sqrt{6\times 62-11}\] \[\sqrt{625}-\sqrt{361}=25-19=6\]
anonymous
  • anonymous
i am confused i just need the solution set
anonymous
  • anonymous
solution is 62
anonymous
  • anonymous
62 works, 2 does not
anonymous
  • anonymous
ok...thx

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