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What is solution in system ? `root(3)(x)` -`root(3)(y)` =0 x+y=2

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lixalixa | Honors

Posted July 15, 2013 at 4:45 PM via web

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What is solution in system ?

`root(3)(x)` -`root(3)(y)` =0

x+y=2

2 Answers | Add Yours

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 15, 2013 at 4:52 PM (Answer #1)

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You should use the following special product in top equation, such that:

`(a - b)(a^2 + ab + b^2) = a - b`

Reasoning by analogy, you should multiply the top equation, both sides, by the factor `(root(3)(x^2) + root(3)(xy) + root(3)(y^2))` , such that:

`(root(3)x - root(3)y)(root(3)(x^2) + root(3)(xy) + root(3)(y^2)) = 0 => x - y = 0`

Replacing `x - y = 0` for `(root(3)x - root(3)y) = 0` in top equation yields:

`{(x - y = 0),(x + y = 2):}`

You need to add the equations to remove the variable y, such that:

`2x = 2 => x = 1`

Replacing 1 for x in the bottom equation yields:

`1 + y = 2 => y = 2 - 1 => y = 1`

Hence, evaluating the solution to simultaneous equations yields `x = 1, y = 1.`

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aruv | High School Teacher | Valedictorian

Posted July 15, 2013 at 5:31 PM (Answer #2)

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`root3x-root3y=0`

`root3x=root 3 y`

Thus

 raise power three both side

`(root 3x)^3=(root 3y)^3`

`x=y`      (i)

also

`x+y=2`    (ii)

Thus from (i),substitute value of y in (ii)

`x+x=2`

`2x=2`

`x=1`

`so y=1`

Thus answer is

x=y=1

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