Chapter 9.3, Problem 34PPS

To determine

To obtain a quadratic equation and fine the two numbers.

Answer to Problem 34PPS

The two numbers are 4 and 5.

Explanation of Solution

Given information :

The sum of the two numbers is 9 and their product is 20 .

Formula used :

Form a quadratic equation by substituting values of the addition and product of the two numbers. Then, solve the given equation to obtain the numbers.

Calculation :

Let the numbers be x and y .

  $x+y=9$

Sum of the numbers.

  $x=9-y$

Rearranging x and y. Let this be equation 1.

  $x\times y=20$

Product of the numbers. Let this be equation 2.

  $=>\left(9-y\right)\times y=20$

Substituting the value of x in equation 1 in equation 2.

  $=>9y-y^2=20$

This can be arranged as

  $=>y^2-9y+20=0$

This is the quadratic equation. Solve this to get the two numbers.

  $=>y^2-4y-5y+20=0$

Breaking the middle term that when multiplied, provides that values of $a{x}^2\times c$ .

  $=>y\left(y-4\right)-5\left(y-4\right)=0$

Arranging the common elements.

  $=>\left(y-4\right)\left(y-5\right)=0$

These are the factors.

Hence the given numbers are 4 and 5.