
Three consecutive positive integers are such that the sum of the square of the first and the product of other two is , the smallest integer is:
Answer
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Hint: Proper conversion of wordings to equation form is must. It is easy to solve such problems with variables, as they can be interrelated easily like to denote they are consecutive in nature.
Complete step-by-step answer:
Here, three consecutive positive integers are such that the sum of the first and product of the other two is .
Let us consider these integers as and such that
Or,
Now, as per the given conditions, we have
, where is first integer, is second integer and is third integer.
Substituting the values of and from equation (1), we get
By transposing values, we get
Applying middle-term split method, we get
Thus, solving the above equation, we get
i.e.,
And,
On cross-multiplication, we get
But as per the given conditions, is a positive integer, so is not applicable.
Thus, and from equation (1), we can calculate other two integers, i.e.,
Similarly,
Hence, the smallest integer out of three consecutive integers, we have .
Note: This type of problem can also be solved with the hit and trial method. Considering values of those three consecutive integers one by one, trying to fit it in given conditions.
Complete step-by-step answer:
Here, three consecutive positive integers are such that the sum of the first and product of the other two is
Let us consider these integers as
Or,
Now, as per the given conditions, we have
Substituting the values of
By transposing values, we get
Applying middle-term split method, we get
Thus, solving the above equation, we get
And,
On cross-multiplication, we get
But as per the given conditions,
Thus,
Similarly,
Hence, the smallest integer out of three consecutive integers, we have
Note: This type of problem can also be solved with the hit and trial method. Considering values of those three consecutive integers one by one, trying to fit it in given conditions.
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