The sum of 2 numbers is 14. The product is 40. What is the largest of numbers?

a + b = 14

a * b = 40

a + b = 14 Subtract a to both sides

a + b - a = 14 - a

b = 14 - a

a * b = 40

a * ( 14 - a ) = 40

14 a - a ^ 2 = 40

- a ^ 2 + 14 a = 40 Subtract 40 to both sides

- a ^ 2 + 14 a - 40 = 40 - 40

- a ^ 2 + 14 a - 40 = 0 Multiply both sides by - 1

a ^ 2 - 14 a + 40 = 0

The solutions are:

a = 4 and a = 10

For a = 10

b = 14 - a = 14 - 10 = 4

For a = 4

b = 14 - 4 = 10

The numbers are:

4 and 10

4 + 10 = 14

4 * 10 = 40

one number ---- x , the larger

the other --- 14-x

x(14-x) = 40
14x - x^2 = 40
x^2 - 14x + 40 = 0

(x-10)(x-4) = 0
x = 10 or x = 4

the two numbers are 10 and 4.

Well, I'm not great with math, but I'll give it a try! Let's call the two numbers x and y. We know that x + y = 14, and xy = 40. Hmmm... let's see... Oh wait, I just got a text from one of the numbers, they said they don't want to be the largest! Looks like it's up to you to figure it out. Good luck!

Let's solve this step by step.

Let's assume the two numbers are x and y.

According to the given information:
x + y = 14 --------(1)
xy = 40 ----------(2)

To find the largest of the two numbers, we need to determine the values of x and y first.

To solve this system of equations, we can use substitution or elimination method.

Let's solve it using the substitution method:
From equation (1), we can isolate x:
x = 14 - y

Now substitute this value of x in equation (2):
(14 - y)y = 40

Expanding and rearranging the equation:
14y - y^2 = 40

Rearranging the equation further:
y^2 - 14y + 40 = 0

Now, we can factorize the quadratic equation:
(y - 4)(y - 10) = 0

Setting each factor to zero:
y - 4 = 0 or y - 10 = 0

Solving each equation separately:
y = 4 or y = 10

Now, substitute these values of y back into equation (1) to find x:
If y = 4, then x = 14 - 4 = 10
If y = 10, then x = 14 - 10 = 4

So, the two possible pairs of numbers are:
(4, 10) and (10, 4)

The largest number among these pairs is 10.

Therefore, the largest of the two numbers is 10.

To find the largest of the two numbers, we can use the information given:

Let's assume the two numbers are x and y. We are given that the sum of the two numbers is 14, so we can write an equation: x + y = 14.

We are also given that the product of the two numbers is 40, so we can write another equation: x * y = 40.

To solve this system of equations, we can use substitution or elimination. Let's solve it using substitution:

From the first equation, we can isolate one variable. Let's solve for x: x = 14 - y.

Now we substitute this expression for x in the second equation: (14 - y) * y = 40.

Simplifying the equation, we get: 14y - y^2 = 40.

Rearranging the equation, we get a quadratic equation: y^2 - 14y + 40 = 0.

Now we can use factoring or the quadratic formula to solve for y. Factoring, we have: (y - 10)(y - 4) = 0.

So, we have two possible values for y: y = 10 or y = 4.

If y = 10, substituting this value back into the first equation, we can solve for x: x + 10 = 14, x = 14 - 10, x = 4.

If y = 4, substituting this value back into the first equation, we can solve for x: x + 4 = 14, x = 14 - 4, x = 10.

So, the possible two numbers are (4, 10) or (10, 4).

Since the question is asking for the largest number, the answer is 10.