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# #16,17 Help. ​

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#16,17 Help.  Feb 12, 2018

#1
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question1:

3√(x+2)^3=27-3

3√(x+2)^3 =24

√(x+2)^3=24/3

√(x+2)^3=8

(x+2)^3=8^5

(x+2)^3=32768

(x+2)=cube root of 32768

x+2=32

x=32-2

x=30   Feb 12, 2018
edited by lynx7  Feb 12, 2018
#2
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√2x+13 -5=x

√2x+13=x+5

2x+13=(x+5)^2

2x+13=(x+5)(x+5)

2x+13=x^2+5x+5x+25

2x+13=x^2+10x+25

2x=x^2+10x+25-13

2x=x^2+10x+12

x=x^2+10x+12/2

x=0.5x^2+5x+6   Feb 12, 2018
edited by lynx7  Feb 12, 2018
edited by lynx7  Feb 12, 2018
edited by lynx7  Feb 12, 2018
#3
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16.

35√ [(x + 2)3 ]  +  3  = 27       subtract 3 from both sides

35√ [(x + 2)3 ]    = 24              divide both sides by 3

5√ [(x + 2)3 ]   =   8                 take each side to the 5/3 power

(x + 2)  =  85/3                       and we can write

(x + 2)  = ( 81/3)5

(x + 2)  =  25

x + 2    =  32                subtract 2 from both sides

x  = 30   Feb 12, 2018
#4
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17.

√[2x + 13 ]  - 5  = x         add 5 to both sides

√[ 2x + 13 ]   =  x + 5        square both sides

2x + 13    = x^2 + 10x + 25       subtract 2x, 13 from both sides

x^2 + 8x + 12  =  0   factor

(x + 6)  ( x + 2)  = 0

Set each factor to 0 and solve for x and we have that

x =  -6     or   x = - 2

The first solution does not solve the original equation

Only the second is good   Feb 12, 2018