Question

3+√5 ही संख्या अपरिमेय संख्या आहे हे सिद्ध करा.

Answer 1

Given :   3+√5 ,  

√5  अपरिमेय संख्या  irrational number

To Find :  3+√5  अपरिमेय संख्या ,  irrational number

Solution:

Assume  that  3+√5 is an rational number

=>  3+√5   = p/q   where p & q are integers q ≠ 0

Squaring both sides

=> 9+ 5  +6√5  = p²/q²

=>  6√5   = p²/q² - 14

=> √5 = (p²/q² - 14)/6

=> √5 = p²/6q²  - 7/3

RHS = Rational

LHS = irrational ( as  ✓5 is an irrational number)

=> LHS ≠ RHS

Hence our assumption is wrong

Hence  3+√5  is not an rational number

=> 3+√5 is irrational number

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Answer 2

Answer:

३+√5 ही संख्या अपरीमेय संख्या आहे हे सिध्द करा