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# Need help with radical equations

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$$n=3+\sqrt{5n-9}$$

$$m=1+\sqrt{5m-5}$$

Just these 2

Oct 29, 2018

### 5+0 Answers

#1
+3

First one:

n-3  = sqrt (5n-9)      square both sides

n^2 - 6n + 9 = 5n-9     simplify

n^2 -11n +18 = 0         (now factor Hint: -9 and -2....or use Quadratic Formula

Second one is similar ......try it! Oct 29, 2018
#2
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I really dont get the first one...

RainbowPanda  Oct 29, 2018
#3
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Okay so for the first one:

n=-(-11)+sqrt[(-11)^2-4*1*18]/2*1

11+sqrt(49)/2=11+7/2=18/2=9

Same thing again but - instead of +

so 11-7/2=4/2=2

So 9,2

Oct 29, 2018
#4
+2

Rearrange the first as

n - 3  =   sqrt [ 5n - 9 ]      square both sides

( n - 3)^2  =  5n  - 9

n^2  - 6n +9   =  5n  -  9        subtract 5n from both sides...add 9 to both sides

n^2  -  11n  +  18  =  0       factor

(n - 9) ( n - 2)  = 0

Set both factors to 0  and solve for n

n - 9  = 0         n  - 2   =  0

n  = 9                n  =  2

Note that the  first answer  in the original equation gives

9  =  3  + sqrt ( 45 - 9)

9  =  3 + sqrt (36)

9  =  3 + 6       true

Note that the second answer in the first equation gives

2 = 3 + sqrt ( 10 - 9 )

2  = 3 + sqrt(1)

2  =    3 + 1     not true

So...the only answer is  n  =  9

Based on this one....can you do the second, RP???   Oct 29, 2018
#5
+1

Ah okay I did both 2 and 9, thanks for your help :)

RainbowPanda  Oct 29, 2018