Easy

Algebra Level 1

Sum of the square of a possitive natural number with with its possitive square root is 2 find out that number


The answer is 1.

Aman Sharma by Aman Sharma , 25, India

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2 solutions

L e t N = X . ∴ X 4 + X = 2 ⟹ X ( X 3 + 1 ) = 1 ∗ 2 ⟹ x = 1 a n d ( x 2 + 1 ) = 2 ∴ X = 1 ∴ N = ± 1 , b u t i t i s + t i v e ∴ N = 1. 1 Let~\sqrt N =X.~~~~~ \therefore~X^4 + X = 2~~~~~\Longrightarrow X(X^3+1) = 1*2 \\ \Longrightarrow ~~~~x=1~~~~and ~~~~(x^2 + 1)=2~~~~~\therefore X=1~\\\therefore~N=\pm1,~but~ it~is~+tive~~~\therefore N=1.\\ \boxed{ 1 }

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Hansraj Sharma
Aug 13, 2014

1^2+1^1/2=2

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