। पूर्ण प्रतियोगिता एकाधिकार से किस प्रकार मिन्न है स्पष्ट कीजिए?
अथवा
Answers
Answer:
वन्दे मातरम्। सुजलाम् सुफलाम् मलयजशीतलाम् शस्यश्यामला मातरम्। वन्दे मातरम्। शुभ्रज्योत्स्नाम् पुलकितयामिनीम् फुल्लकुसुमित द्रुमदलशोभिनीम् सुहासिनीम् सुमधुर भाषिणीम् सुखदाम् वरदाम् मातरम्।। वन्दे मातरम्।
Explanation:
Question : Prove that√5 is irrational.
Answer :
Let us assume that √5 is a rational number.
Sp it t can be expressed in the form p/q where p,q are co-prime integers and q≠0
⇒√5=p/q
On squaring both the sides we get,
⇒5=p²/q²
⇒5q²=p² —————–(i)
p²/5= q²
So 5 divides p
p is a multiple of 5
⇒p=5m
⇒p²=25m² ————-(ii)
From equations (i) and (ii), we get,
5q²=25m²
⇒q²=5m²
⇒q² is a multiple of 5
⇒q is a multiple of 5
Hence, p,q have a common factor 5. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number
√5 is an irrational number
Hence proved
✌NISHU HERE✌✌