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Prove that 5-2√5 is irrational |
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Answer» Answer: Let us assume on the CONTRARY that 5+ ROOT 2 is rational. Then, there exist co-prime a and b(b not equal to 0), such that 5+ root 2= a by b = root 2= a by b--2 = root 2 =a--2b by b = root 2 is rational [Therefore, 5, a & b are INTEGERS, a--2b by b is a rational number] This contradicts the fact the root 2 is irrational. The contradiction has arisen because of our incorrect ASSUMPTION that 5+ root 2 is rational. Hence, 5+root 2 is irrational. Hope this helps :D |
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