show that 3√5-1 is not a rational number
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3√5-1 is a irrational number because it cannot be represented in the p/q form.
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Solution:
Let the 3√5-1 be a rational number
hence, 3√5-1 can be written in p/q form
● 3√5-1 = p/q
● √5 = p/q × 1/3 +1
● √5 = p/3q+1
Hence w.k.t √5 is an irrational number
Therefore, p/3q+1 is also irrational number.
Hence, 3√5-1 is an irrational number. therefore our assumption is wrong.
Thanks for asking
Let the 3√5-1 be a rational number
hence, 3√5-1 can be written in p/q form
● 3√5-1 = p/q
● √5 = p/q × 1/3 +1
● √5 = p/3q+1
Hence w.k.t √5 is an irrational number
Therefore, p/3q+1 is also irrational number.
Hence, 3√5-1 is an irrational number. therefore our assumption is wrong.
Thanks for asking
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