the product of 2 consecutive positive integers is 306. form the quadratic equation to the integers,if x denotes the smaller integer.
Answers
• Let two consecutive positive integers be (x) and (x + 1)
》 The product of two consecutive positive integers is 306.
According to question,
=> x(x + 1) = 306
=> x² + x = 306
=> x² + x - 306 = 0
The above equation is in the form ax² + bx + c.
So, let's solve it by factorization.
Here..
a = 1, b = 1 and c = -306
Find a number whose sum is 'b' i.e. (1) and product is 'c' i.e. (-306).
=> x² + 18x - 17x - 306 = 0
The numbers are (+18) and (-17).
As the sum of (+18) and (-17) is (1) and product of (+18) and (-17) is (-306)
=> x(x + 18) -17(x + 18) = 0
x + 18 is common. So, write it one time.
=> (x - 17) (x + 18) = 0
First take.. x - 17 = 0
=> x - 17 = 0
=> x = 17
Now..
=> x + 18 = 0
=> x = - 18
(Neglected)
We have x = 17.
We have to find a two positive number. And the numbers let by us are x and x + 1.
So,
=> x = 17
=> x + 1 = 17 + 1 = 18
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Two positive integers are 17 and 18.
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☆ VERIFICATION :
From above calculations we have x = 17 and x + 1 = 18
Put value of them in : x(x + 1) = 306
=> 17(18) = 306
=> 306 = 306
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