Square both ways

Algebra Level 1

What is the positive value x x such that x 4 + 2 x 3 + 3 x 2 + 2 x + 1 = 49 x^4+2x^3+3x^2+2x+1=49 ?


The answer is 2.

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谦艺 伍 by 谦艺 伍 , 31, Malaysia

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1 solution

Alex Li
Apr 14, 2015

Note that x 4 + 2 x 3 + 3 x 2 + 2 x + 1 = ( x 2 + x + 1 ) 2 x^4+2x^3+3x^2+2x+1=(x^2+x+1)^2 . ( x 2 + x + 1 ) 2 = 49 = > x 2 + x + 1 = ± 7 = > x = 2 , − 3 (x^2+x+1)^2=49=>x^2+x+1=\pm7=>x=\boxed{2, -3}

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sorry for the mistake of the problem

谦艺 伍 - 6 years, 2 months ago

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Nice question. Note that as the problem creator, you can edit your own problems by selecting "Edit problem" from the "dot dot dot" menu.

I've edited the phrasing of your problem to indicate that we only want the positive answer.

Calvin Lin Staff - 6 years, 2 months ago

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Thank you!

谦艺 伍 - 6 years, 1 month ago

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