SOLUTION: at present sohan's age is 7 more than a square number and 6 less than it immediate next square number.in how many years sohan will be 80 years?

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Question 760546: at present sohan's age is 7 more than a square number and 6 less than it immediate next square number.in how many years sohan will be 80 years?
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
Sohan's age is 7 more than a square number.
So, if x is the age,
x+=+n%5E2+%2B+7 for some number n.
Next number = n+1
x is also given to be 6 less than the next square number.
i.e. x+=+%28n%2B1%29%5E2+-+6
Equating the two values of x,
n%5E2+%2B+7+=+%28n%2B1%29%5E2+-+6
Expanding (n+1)^2
n%5E2+%2B+7+=+n%5E2+%2B+2%2An+%2B+1+-+6+=+n%5E2+%2B+2%2An+-+5
Removing n^2 from both sides
7+=+2%2An+-+5
i.e
2%2An+=+12
i.e.
n+=+6
So Sohan's age is 6%5E2+%2B+7+=+43 years.
In how many years will Sohan be 80 years old?
Sohan will be 80 in another 80+-+43+=+37 years.