the product of two integers is -144. and sim of the integer is -7 . fi

1.	the product of two integers is -144. and sim of the integer is -7 . find the smallest number. Please explain the answer
Answer» Concept:- Here, We have given the product of two integers and the sum of two integers. We have to find the smallest integer in both integers. Let's find Given:- Product of two integers is -144. Sum of two integers is -7. To Find:- Smallest NUMBER in both the integers ? Solution:- Here, Let the one integer be x. Then, ANOTHER integer will be y. Now, According to the question we have, $\sf{xy = -144}$ -------------- (i) $\sf{x + y = -7}$ --------------- (ii) By SOLVING equation (ii) we get, $\sf{x = -7 - y}$ ----------- (III) Now, Putting the equation (iii) in equation (i) we get, $\sf{\Longrightarrow (-7 - y)y = -144}$ $\sf{\Longrightarrow -(7y + y^{2}) = -144}$ [ Taking (-) common ] $\sf{\Longrightarrow y^{2} + 7y = 144}$ $\sf{\Longrightarrow y^{2} + 7y - 144 = 0}$ By middle term splitting, $\sf{\Longrightarrow y^{2} + 16y - 9y - 144 = 0}$ $\sf{\Longrightarrow y(y + 16) - 9(y + 16) = 0}$ $\sf{\Longrightarrow (y + 16) (y - 9) = 0}$ EQUATING both the equations separately we get, $\Longrightarrow \begin{array}{c\|c} \bf y - 9 = 0 & \bf y + 16 = 0\end{array}$ $\Longrightarrow \begin{array}{c\|c} \bf y = 9 & \bf y = -16\end{array}$ Hence, The smallest number is -16.