prove that 5+ root5 is an irrational number.
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prove that 5+ root5 is an irrational number.
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To Prove :-
Let us suppose that 5 + √5 is not irrational
=> 5 + √5 is rational.
Let we suppose that 5 + √5 = x/y, where x and y are positive integers such that HCF of a and b is 1.
Now, as x and y are intergers, so x - 5y is also an integer.
which is contradiction to the fact that √5 is irrational.
Hence, our assumption is wrong.