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How can √((x^4)+(3x^2))-(x^2) become 3/2?    

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ebbacarlsson | Student, Undergraduate | eNotes Newbie

Posted October 30, 2012 at 1:49 PM via web

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How can √((x^4)+(3x^2))-(x^2) become 3/2?

 

 

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted October 30, 2012 at 6:24 PM (Answer #1)

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You need to complete the square `x^4 + 3x^2`  using the formula `(a+b)^2 = a^2 + 2ab + b^2` .

`x^4 + 3x^2 = a^2 + 2ab => {(x^4 = a^2 => x^2=a),(3x^2 = 2x^2b => b = 3/2):}`

Completing the square yields:

`(x^4 + 3x^2 + 9/4) - 9/4= (x^2 + 3/2)^2 - 9/4`

Hence, substituting `sqrt(x^4 + 3x^2) - x^2 = sqrt((x^2 + 3/2)^2 - 9/4) - x^2 != 3/2`

Hence, completing the square yields `(x^2 + 3/2)^2 - 9/4` , thus `sqrt(x^4 + 3x^2) - x^2 = sqrt((x^2 + 3/2)^2 - 9/4) - x^2 != 3/2.`

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parvesh | Student, Grade 11 | eNoter

Posted October 30, 2012 at 2:47 PM (Answer #2)

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take x^2 on RHS

SQUARE on both sides

so LHS=(x^4 + 3x^2)

and RHS=( x^4 + 3x^2 +9/4)

on solving it gives 9/4 = 0  which is impossible.

SO WE CAN SAY THAT THIS EQUATION HAVE NO SOLUTIONS

 

 

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