Two numbers that multiplied together give me 10 and the difference of the two numbers is -2?

10/(1+√11),  1+√11 and 10/(1-√11) and  1-√11

Step-by-step explanation:

Let x be the first number and y the second number

two numbers that multiplied together give me 10

x*y = 10

and the difference of the two numbers is -2?

x-y = -2

we can write x in terms of y so we only have one variable y

x-y =-2 , add y to both sides

x-y+y = y -2, combine like terms

x= y-2

x*y = 10, substitute x=y-2

(y-2)y = 10, distribute in parenthesis

y² -2y-10 = 0, subtract 10 from both sides

We can use the quadratic formula to solve y² -2y-10 = 0

y = (-b±√b²-4ac)/2a, where a= 1, b= -2, c= -10

y = (2±√4+4*1*10)/2

y = (2±√44)/2

y= (2±2√11)/2

y= 1±√11

x*y = 10, divide both sides by y

x= 10/y

x= 10/(1±√11)

Check :

x*y = 10

[10/(1±√11)] * (1±√11) = 10

⇒[10/(1+√11)] * (1+√11) = 10✅

⇒[10/(1-√11)] * (1-√11) = 10✅

⇒[10/(1+√11)] * (1-√11) = 10❌

⇒[10/(1-√11)] * (1+√11) = 10❌

x-y = -2

⇒

[10/(1+√11) ] -(1+√11) =

[10 -(1+√11 )(1+√11 )]/ (1+√11 ) =

[10 - (1+11+2√11)]/ (1+√11) =

(10-12 -2√11) / (1+√11) =

(-2 -2√11) / (1+√11) =

-2(1+√11)/ (1+√11) =

-2 ✅

⇒

[10/(1-√11) ] -(1-√11) =

[10 -(1-√11 )(1-√11 )]/ (1-√11 ) =

[10 - (1+11-2√11)]/ (1-√11) =

(10-12 +2√11) / (1-√11) =

(-2 +2√11) / (1-√11) =

-2(1 -√11)/ (1-√11) =

-2 ✅

i have no answer for this maybe o 7 units