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InterviewSolution
| 1. |
Prove 2+√5 is irTional |
| Answer» We preassume that\xa0{tex}2 + \\sqrt 5 {/tex}\xa0is a rational number.So it can be written as\xa0{tex}\\frac{a}{b}{/tex}, where a, b are co-prime integers and b is not zero.The new equation will be as below:\xa0{tex}\\implies 2 + \\sqrt 5 = \\frac{a}{b}{/tex}So, we will get\xa0{tex}\\sqrt 5 = \\frac{a}{b} - 2{/tex}As we know that 2 and {tex}\\frac{a}{b}{/tex}\xa0are rational numbers, their difference will be rational number only.on the other hand,\xa0{tex}\\sqrt 5 {/tex}\xa0is an irrational number and it can not be written as\xa0{tex}\\frac{a}{b}{/tex}.So, this contradicts the fact that\xa0{tex}\\sqrt 5 {/tex} is a rational number.\xa0Therefore our assumption is wrong and {tex}2 + \\sqrt 5 {/tex}\xa0is irrational. | |