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Solve  \(\large (7x-2)^{1/3} + (7x+5)^{1/3} = 3 \)

 Jul 9, 2020
 #1
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Solution: 

 

(7x-2)^1/3+(7x+5)^1/3=3  >>> x= 3/7  (Decimal:  x=0.42857...)  

 

Steps:

 

(7x-2)^1/3+(7x+5)^1/3=3 

 

1) Rewrite the equation with (7x-2)^1/3=u and x= u^3+2/7

u+(7(u^3+2/7)+5)^1/3=3

 

2) Solve u+(7(u^3+2/7)+5)^1/3=3 :  u=1

 

3) Substitute back u=(7x-2)^1/3, solve for x

(7x-2)^1/3=1  :  x=3/7

 

4) Check answer:

((7*3/7)-2)^1/3+((7*3/7)+5)^1/3=3  <<

 

 

I hoped that helped, my explanation might be a bit confusing...sorry if it is. I'm a newby, not the best at this stuff...

 

blushcheekywink

 Jul 9, 2020

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