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Find the value of x √(3+x) + √(2x-1)=5

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mark222 | Student, Undergraduate | Honors

Posted February 9, 2012 at 9:46 AM via web

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Find the value of x

√(3+x) + √(2x-1)=5

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted February 9, 2012 at 10:25 AM (Answer #1)

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`sqrt(3+x) + sqrt(2x-1) = 5`

`` Square both sides.

`==gt (sqrt(3+x) + sqrt(2x-1))^2 = 5^2 `

`==gt (3+x) + 2sqrt((3+x)(2x-1)) + (2x-1) = 25 `

`==gt 3x +2 + 2sqrt(2x^2 +5x -3) = 25 `

`==gt 2sqrt(2x^2 + 5x -3) = -3x + 23`

`` Square both sides

`==gt 4(2x^2 + 5x -3) = 9x^2 - 138x + 529 `

`==gt 8x^2 + 20x - 12 = 9x^2 - 138x + 529`

`` Combine like terms.

`==gt x^2 -158x + 541 = 0 `

`==gt x= (158+-151)/2 `

`==gt x1= (158+151)/2 = 154.5 `

`==gt x2= (158-151)/2 = 7/2 = 3.5`

`` Then we have two solutions:

==> x = { 154.5, 3.5}

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