What two numbers add together to make 11 yet multiply together to make 5.?

Answer 1

[07]
Let the numbers be x andy
By the problem,
x+y=11.......(1)
xy=5...........(2)
We know that (x-y)^2
=(x+Y)^2-4xy
=(11)^2-4*5
=121-20
=101
Therefore x-y= sqrt101
Now,we have two equations
x+y=11 and
x-y=sqrt101
By solving ,we get
x=(11+sqrt101)/2 and y=(11-sqrt101)/2
Therefore,the nos are (11+sqrt101)/2 and (11-sqrt101)/2

Answer 2

Let's let the numbers be x and y:
x + y = 11
xy = 5

Solve the first for y:
y = 11 - x

Substitute this into the second equation:
x(11 - x) = 5

Now expand out:
11x - x² = 5

Let's get everything on one side (add x², subtract 11x):
x² - 11x + 5 = 0

You can solve this with the quadratic formula:

x = [11 ± sqrt( (-11)² - 4*5 ) ] / 2
x = [11 ± sqrt( 121 - 20 ) ] / 2
x = [11 ± sqrt( 101 ) ] / 2

The two numbers are:
(11 - √101) / 2 ≈ 0.475062189
(11 + √101) / 2 ≈ 10.5249378

Double checking our answers with the approximations:
0.475062189 + 10.5249378 = 10.99999999 --> 11

Multiplying:
0.475062189 * 10.5249378 = 4.99999999 --> 5

The slight errors at the end are because we are using an approximation of the answer.

The answers are:
(11 - √101) / 2
(11 + √101) / 2

Answer 3

You could take 5 and 1. You didn't specify if a number could only be used once!

5+5+1 = 11
AND
1 x 5 = 5

Answer 4

Set up a system of equations.
x+y=11
x*y=5
Solve
1. y=x/5
2. x + x/5 = 11 (substitution)
3. x = (11+ square root of 101)/2 or (11 - square root of 101)/2

The two numbers are simply the same as the solutions of x.

Answer 5

x + y = 11 or y = 11 - x

xy = 5
now substitute y from the first equation into the second

x(11-x) = 5

-x^2 + 11x = 5 or

x^2 - 11x + 5 = 0


now solve for x, then for y

Answer 6

given
a+b=11
ab=5

we can determine that
a(11-a)=5
a^2-11a+5=0

therefore
a = [11 +/- sqrt(101)]/2
if we let a be the result using +, then b will be the result with -, and vice versa. in other words, the two numbers are
[11 +/- sqrt(101)]/2

that is to say,
[11 + sqrt(101)]/2
and
[11 - sqrt(101)]/2

very rough approximations are 10.5 and 0.5
clearly their sum is 11, the product of these
approximations is 5.25, but if you don't use approximations
(or more accurate approximations) you'll get closer to 5 (or exactly 5 if you use the closed form expressions)

if you want, i can rattle on and on, adding more and more to this answer.

Answer 7

puzzling made a sign mistake
you get x^2 - 11x + 5 = 0
and so the two numbers are
[11 + √101]/2 and [11 - √101]/2
~~

Answer 8

no numbers multiply to make 5!

Answer 9

ok you have 2 equations
(1) x+y=11 and
(2) x*y=5

i hope from there you can solve it, but if not, i will post the answer (you have to do the work) in about a minute

but i guess puzzling did the work for you... so nv

Answer 10

if u have to have the same 2 numbers, good luck and have fun trying to make the impossible possible