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Solve for x: (x^2+x^2)/(x+1)^2=3

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aniljha127 | High School Teacher | (Level 1) eNoter

Posted June 9, 2012 at 12:54 AM via web

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Solve for x: (x^2+x^2)/(x+1)^2=3

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 9, 2012 at 2:37 AM (Answer #1)

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The equation `(x^2+x^2)/(x+1)^2=3` has to be solved for x.

`(x^2+x^2)/(x+1)^2=3`

=> `(x^2+x^2) = 3*(x+1)^2`

=> `2x^2 = 3x^2 + 6x + 3`

=> `x^2 + 6x + 3 = 0`

`x1 = (-6 + sqrt(36 - 12))/2 = -3 + sqrt 6`

`x2 = -3 - sqrt 6`

The solution of the equation is `-3 + sqrt 6` and `-3 - sqrt 6`

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elekzy | Student, Grade 11 | (Level 1) Valedictorian

Posted June 9, 2012 at 1:19 AM (Answer #2)

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first of all, to remove the fraction, multiply both sides by (x+1)^2

x^2+x^2=3(x+1)^2

simplify

 2x^2=3(x^2+2x+1)

2x^2=3x^2+6x+3

collect like terms

0=3x^2-2x^2+6x+3

0=x^2+6x+3

this cannot be simplified by factoring...so, its best to use the quadratic formula

 

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