Solve application problems using quadratic equations. 1. A positive real number is 4 less than another. When 8 times the larger is added to the square of the smaller, the result is 96. Find the numbers.

The amount given by the sum of numbers can be presented in an equation

form from which the value of each number can be obtained.

The large number is 4·√5, the smaller number is 4·(√5 - 1)

Reason:

Let x represent the large number, we have;

The smaller number = x - 4

8 × x + (x - 4)² = 96

8·x + (x - 4)² = 96

Required:

The values of the numbers

Solution:

8·x + (x - 4)² = 8·x + x² - 8·x + 16 = 96

8·x - 8·x + x² + 16 = 96

x² + 16 = 96

x² = 96 - 16 = 80

x = ±√(80) = ±4·√5

Given that the numbers are positive, we have;

The large number, x = 4·√5

The smaller number = x - 4 = 4·√5 - 4

The smaller number = 4·√5 - 4 = 4·(√5 - 1)

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Hello, let's  note a the positive real number.

A positive real number is 4 less than another.

So, the other number is a - 4

When 8 times the larger is added to the square of the smaller, the result is 96.

So, we need to solve the following equation.

Let's do it!

As a is positive, there is only one solution which is.

Thank you.

it would be 6xy and -16xy.

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