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

- anonymous

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

- katieb

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- anonymous

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

- anonymous

Yes the equation is correct

- 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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## More answers

- anonymous

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

- 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

Thx

- anonymous

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

- anonymous

and 5+1=6

- anonymous

So would the sol set be 5,1

- anonymous

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

- 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

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

- anonymous

K :-)

- anonymous

62

- anonymous

is the answer

- anonymous

would you like a worked out solution?

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

so is there only one solution of 62

- anonymous

sorry my computer is slow

- anonymous

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

- anonymous

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

- anonymous

introduced a false solution when you squared

- anonymous

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

- anonymous

thx u

- anonymous

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

- anonymous

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

- anonymous

factor
\[(x-62)(x-2)=0\]
\[x=62\] or \[x=2\]

- 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

negatives on both?? thx

- anonymous

62 will work but only 62, not 2.

- anonymous

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

- anonymous

you have to plug it into the original equation

- anonymous

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

- anonymous

i am confused i just need the solution set

- anonymous

solution is 62

- anonymous

62 works, 2 does not

- anonymous

ok...thx

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