দুটি ধনাত্মক অখণ্ড সংখ্যার অন্তর 3 এবং তাদের বর্গের সমষ্টি 117; সংখ্যা দুটি হিসাব করে লিখি।
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Given : The difference between two positive integers is 3 and the sum of their squares is 117;
To Find : the numbers
Solution:
Let say two numbers are a , a + 3
sum of their squares is 117;
=> a² + ( a + 3)² = 117
=> a² + a² + 6a + 9 = 117
=> 2a² + 6a - 108 = 0
=> a² + 3a - 54 = 0
=> a² + 9a - 6a - 54 = 0
=> a( a + 9) - 6( a + 9) = 0
=> (a - 6)(a + 9) = 0
=> a = 6 , a = - 9
a is positive
Hence a = 6
a + 3 = 9
Two numbers are 6 and 9
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