The product of two numbers is 154. If the difference between the sum o

1.	The product of two numbers is 154. If the difference between the sum of two numbers is 3, find the numbers
Answer» ANSWER : The TWO numbers are -11 or 14 and -14 or 11. EXPLANATION : GIVEN :- Product of two numbers is 154. Difference between two numbers is 3. TO FIND : The two numbers. SOLUTION : Let the two numbers be x and y. Product of two numbers= 154 Difference between two numbers=3 According to the question, $\sf{xy=154...........(i)}$ $\sf{x-y=3}$ $\implies\sf{x=3+y.........(ii)}$ ★Taking (i) no. equation★ $\sf{\:\:\:\:xy=154}$ † Putting x=3+y from the eq.(ii) † $\implies\sf{(3+y)y=154}$ $\implies\sf{3y+y^2=154}$ $\implies\sf{y^2+3y-154=0}$ $\implies\sf{y^2+(14-11)y-154=0}$ $\implies\sf{y^2+14y-11y-154=0}$ $\implies\sf{y(y+14)-11(y+14)=0}$ $\implies\sf{(y+14)(y-11)=0}$ Either, y+14 = 0 →y = -14 Or, y-11 = 0 →y = 11 † Putting y = -14 and y =11 in eq.(ii) † ➪ x = 3+y → x = 3-14 → x = -11 ➪ x = 3+ y → x = 3+11 → x = 14 x = 14 or -11 y = 11 or -14 Therefore, the two numbers are 14 or (-11) and 11 or (-14).