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Prove that 1/3-2√5 is an irrational …

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Prove that 1/3-2√5 is an irrational number

Posted by Jyoti Das 7 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Ishu Ishu 7 years, 3 months ago

If possible let (1/2 - √5/3) be a rational number x 1/2-√5/3 => x making denominator equal (3-2√5)/6 => x 3-2√5 = 6x 3-6x = 2√5 2(1-2x)/2 = √5 1-2x = √5 since , x is rational number (by our supposition) 2x is also rational 1 is rational and we know that , difference of 2 rationals is rational number so, this tells us that √5 is also rational but , √5 is irrational thus , our supposition is wrong so x is not rational , and x = 1/2 -√5/3 so, 1/2 - √5/3 is irrational hope this helps Read more on Brainly.in - https://brainly.in/question/1462562#readmore

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CBSE > Class 10 > Mathematics