A natural number is greater than the older by 5 . The sum of their squares is 73. Find the numbers
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Let the two natural numbers be a and b
a^2+b^2=73.......(1)
a−b=5
a=b+5..............(2)
(b+5)^2+b^2=73.........From (1) and (2)
b^2+10b+25+b^2=73
2b^2+10b−48=0
b^2+5b−24=0
(b+3)(b−8)=0
∴b=8
Hence, a=3
Thus, the two numbers are 3 and 8
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Answer:
The two numbers are 3 and 8
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