Question

The sum of two integer is -11 and their product is -80. What are the integers

Answer 1

Answer:

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Answer 2

Answer:

-16 and 5

Step-by-step explanation:

let the two nos be x and y

Hence,

$x + y = - 11 \\ x y= - 80$

So,

$x = \frac{80}{y}$

Substitute in the expression.

$x + y = - 11 \\ \frac{80}{y} + y = - 11 \\ \frac{80 + {y}^{2} }{y} = - 11 \\ {y}^{2} +11y + 80 = 0 \\ y = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} \\ y = \frac{ - 11 + - \sqrt{121 - 4(1)(80)} }{2} \\ y = \frac{ - 11 + - \sqrt{1} }{2} \\ y = \frac{ - 11 + 1}{2} \\ y = 5$

or $y = \frac{ - 11 - 1}{2} \\ y = - 6$

Therefore,

$xy = - 80 \\ x(5) = - 80 \\ x = - 16$

or

$xy = - 80 \\ x( - 6) = - 80 \\ x = 13.333333....$

x= 13.333... or -16

y= -6 or 5

• But look carefully,x= 13.3333 when added any value of y will not give -11 as their sum.
• Also, y= -6 added to any value of x will not as the sum -11.

Hence the nos are -16 and 5 which satisfies all the equations.