Find a pair of integers whose product is -35 and whose difference is 12.
Answers
Given :
- Product of two integers = - 35
- Difference of the two integers = 12
To find :
- The two integers
Solution :
Let,
- The first integer = x
- The second integer = y
According to the first condition given,
⇒ First integer × Second integer = - 35
⇒ (x) × (y) = - 35
⇒ xy = - 35 -----(1)
According to the second condition given,
⇒ First integer – Second integer = 12
⇒ x - y = 12 -----(2)
Taking equation (1) :
⇒ xy = - 35
⇒ x = - 35/y -----(3)
Substituting (3) in equation (2) :
⇒ x - y = 12
⇒ - 35/y - y = 12
⇒ (-35 - y²)/y = 12
⇒ - 35 - y² = 12y
⇒ y² + 12y + 35 = 0
A quadratic equation is formed whose product is 35y².
• Splitting the middle term :
⇒ y² + 7y + 5y + 35 = 0
• Taking common :
⇒ y(y + 7) + 5(y + 7) = 0
⇒ (y + 5)(y + 7) = 0
⇒ (y + 5) = 0 or (y + 7) = 0
⇒ y = - 5 or y = - 7
Substituting the value of y in equation (1) :
When y = - 5, then x :-
⇒ xy = - 35
⇒ x × (-5) = - 35
⇒ x = - 35/-5
⇒ x = 35/5
⇒ x = 7
When y = - 7, then x :-
⇒ xy = - 35
⇒ x × (-7) = - 35
⇒ x = - 35/-7
⇒ x = 35/7
⇒ x = 5
Therefore,
The pair of integers is :-
- When the first number = 7, then the second number = - 5
- When the first number = 5, then the second number = - 7
Step-by-step explanation:
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