the product of two consecutive integers is 306 . we need to find the integers?
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the product of two consecutive integers is 306 . we need to find the integers?
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Answer:
Let x and x+1 be the two consecutive positive integers .
Therefore, x (x+1) =306.
Or, x^2 +x -306 = 0.
Or, x^2 +(18-17)x - 306 = 0
Or, (x+18)(x-17) = 0
We get x =17,and -18.
so, the two consecutive positive integers are 17 and 18.
QUESTION :-
The product of two consecutive integers is 306 . we need to find the integers?
ANSWER :-
The product of two consecutive integer = 306
To Find -
Consecutive integer whose product is 306.
Now,
Let the two consecutive integers be (x) and (x+1).
[tex]x(x + 1) = 306 \\ = > {x}^{2} + x \: = 306 \\ = > {x}^{2} + x - 306 = 0 \\ = > {x}^{2} + 18x - 17x - 306 = 0 \\ = > x(x + 18) - 17(x + 18) = 306 \\ = > (x + 18)(x - 17) = 0 \\ = > x + 18 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: and \: \: \: \: \: x - 17 = 0 \\ = > x = - 18 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: and \: \: \: \: x \: = 17 \: [/tex]
Hence,
Case 1:- when x = 17
The first integer be 17.
& other be (x+1) = 17+1 = 18.
Case 2:- when x = - 18
The first integer be - 18
& other be (x+1) = - 18 +1 = - 17
____________________
Thank you for the question !