1 equation, n variables

Algebra Level 3

x 1 − 1 2 + 2 x 2 − 2 2 + … + n x n − n 2 = 1 2 [ x 1 + x 2 + … + x n ] \sqrt{x_{1}-1^{2}} + 2 \sqrt{x_{2}-2^{2}} + \ldots + n \sqrt{x_{n}-n^{2}} = \frac{1}{2} \left [ x_{1} + x_{2}+ \ldots + x_{n} \right ]

Then which of the following is true?

x n = n x_{n}=n x n = 2 n 2 x_{n}=2n^{2} x n = 2 n x_{n}=2n Cannot be determined x n = n 2 x_{n}=n^{2}

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Aditya Lalbondre by Aditya Lalbondre , 22, India

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1 solution

Anirban Jana
Apr 25, 2015

each term on the LHS containing x1 , x2, x3 ......should finally yield (x1/2 ),(x2/2) ,(x3 /2),..... as each term is unique and there is only one source(term) from which a particular variable comes, so Xn/2=n[(Xn - n^2)^1/2] solving this we get Xn=2n^2

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