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Question Number 1034 by 123456 last updated on 21/May/15

x = i + f, i \in N, f \in [0, 1)

x^{2} = {(i + f)}^{2} = i^{2} + 2 i f + f^{2}

x \in R_{+}

i + 2 f = 2 \Rightarrow x^{2} = 2 i + f^{2}

2 i f = 0 \Rightarrow x^{2} = i^{2} + f^{2}

Answered by prakash jain last updated on 21/May/15

2 i f = 0 \Rightarrow i = 0 \lor f = 0

∵ f < 1, i + 2 f = 2 \Rightarrow i > 0

f = 0, i = 2

x^{2} = 2^{2} \Rightarrow x = \pm 2