Simplifying Square Root Equations

[frozen7]

Simple Maths Problem...:)

How to solve this equation?
( 3 ((x+1)^1/2))^1/2 = (3x-5)^1/2

 

[geosonel]

How to solve this equation?
( 3 ((x+1)^1/2))^1/2 = (3x-5)^1/2

first, square both sides
then, square both sides again
then, solve quadratic
then check answers (discard non-solutions)

 

[frozen7]

I can't find the correct answer in this way...the answer should be (13+(105)^1/2)/6 actually...

 

[geosonel]

I can't find the correct answer in this way...the answer should be (13+(105)^1/2)/6 actually...

you'll get that answer (plus 1 other that must be discarded).
show your work if you still have trouble

 

[frozen7]

Can you please show me the work? I still can't find it...thanks...

 

[Knavish]

I'm not sure what you're not getting... Square both of the sides twice, and come up with the quadratic 9x^2-39x+16. The solution for this will of course contain two answers, but one will be invalid.

 

[frozen7]

ya...i get this final equation...but i get the value of x= (13 +/- (233)^1/2) / 6

 

[geosonel]

How to solve this equation?
( 3 ((x+1)^1/2))^1/2 = (3x-5)^1/2

square first time:
3 ((x+1)^1/2) = (3x-5)
square second time:
9(x+1) = 9x^2 - 30x + 25
rearrange:
9x^2 - 39x + 16 = 0
solve quadratic:
x = (1/18)*(39 ± (1521 - 576)^(1/2))
x = (1/18)*(39 ± (945)^(1/2))
divide num & denom by 3:
x = (13 ± (105)^1/2)/6
x = 3.8745 or 0.4588
check answers in problem eq:
0.4588 - no good (discard)
3.8745 - ok

 

[frozen7]

oh..thanks...just meet some mistakes...