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Solve for x. 2x^4  +3 = 165

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kristenmarieb... | Student, Grade 10 | Valedictorian

Posted April 14, 2013 at 3:29 AM via web

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Solve for x.

2x^4  +3 = 165

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rakesh05 | High School Teacher | (Level 1) Assistant Educator

Posted April 14, 2013 at 5:45 AM (Answer #2)

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Given   `2x^4+3=165`

or,     `2x^4=165-3`

or,      `2x^4=162`

or,      `x^4=162/2=81`

or,    `x^4-81=0`

or,     `x^4-3^4=0`

or,      `(x^2-3^2)(x^2+3^2)=0`     

As   `x^2-a^2=(x-a)(x+a)` .

or,   `(x-3)(x+3)(x+3i)(x-3i)=0`

`(x-3)=0rArrx=3` ,  `(x+3)=0rArrx=-3` ,

`(x+3i)=0rArrx=-3i,`     `(x-3i)=0rArr x=3i` .

So,  `x=+-3`   and   `x=+-3i` .

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 17, 2013 at 5:08 AM (Answer #3)

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The equation 2x^4 +3 = 165 has to be solved for x.

2x^4 +3 = 165

=> 2x^4 + 3 - 3 = 165 - 3

=> 2x^4 = 162

=> x^4 = 81

=> `x^2 = +-9`

For x^2 = 9, `x = +-3`

For x^2 = -9, `x = +-3*i`

The solutions of the equation are `{-3*i, 3*i, -3, 3}`

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