26 10 18 14 2226 3034 3842 4650 5458 में से किन तीन संख्याओं का योग 60 होगा
Answers
प्रश्न :- 2, 6, 10, 18, 14, 22, 26, 30 , 34, 38, 42, 46 , 50, 54 , 58 में से किन तीन संख्याओं का योग 60 होगा ?
उतर :-
दी हुई संख्याएं = 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54 और 58 .
जैसा की हम देख सकते है दी हुई सभी संख्याएं सम संख्या है l अब हमें बताना है कि इनमें से किन तीन संख्याओं को जोड़े की 60 योग मिले l
अत,
→ 2² + 6 + 50 = 4 + 6 + 50 = 60
→ 2² + 10 + 46 = 4 + 10 + 46 = 60
→ 2² + 14 + 42 = 4 + 14 + 42 = 60
→ 2² + 18 + 36 = 4 + 18 + 36 = 60
→ 2² + 22 + 34 = 4 + 22 + 34 = 60
→ 2² + 26 + 30 = 4 + 26 + 30 = 60
- यहां पर 2² (4) पहली संख्या को ले कर बाकी दो संख्या जिनका जोड़ 56 था वो लिख दी गई है l
इसी प्रकार हम (6² = 36) का प्रयोग करके भी कुछ संख्याएं पता कर सकते है जो निम्न है :-
→ 6² + 2 + 22 = 60
→ 6² + 10 + 14 = 60
→ 6² + 6 + 18 = 60
अत बताई गई निम्न कुछ संख्याओं से हम जोड़ 60 निकाल सकते है l
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Given : 2,6,10,14,18,22,26,30,34,38,42,46,50,54,58
To find : 3 numbers such that sum = 60
Solution:
26 + 34 = 60 ( 2 , 6 & 34 number used)
2,6,10,14,18,22,26,30,34,38,42,46,50,54,58
This is an AP
with d = 4 a = 2
an = a + (n-1)d
=> an = 2 + ( n - 1)4
=> an = 2 + 4n - 4
=> an = 4n - 2
Any term will be of form 4n - 2
if we add any three term
then sum would be 4a - 2 + 4b - 2 + 4c - 2
= 4(a + b + c) - 4 - 2
= 4(a + b + c - 1) - 2
= 4k - 2
Sum = 4 k - 2
60 = 4 * 15
Hence 4k - 2 can not be equal to 4 * 15
Hence sum can not be equal to 60
Hence its not possible to add 3 numbers to get 60
but if we do not use simple maths
then we can use three numbers
2 , 6 & 34
26 + 34
= 60
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