## A positive real number is 4 less than another. If the sum of the squares of the two numbers is 72, then find the numbers.

Question

A positive real number is 4 less than another. If the sum of the squares of the two numbers is 72, then find the numbers.

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5 months 2021-08-15T00:42:02+00:00 2 Answers 27 views 0 Step-by-step explanation:

Let the large number be . We can represent the smaller number with . Since their squares add up to 72, we have the following equation: Expand using the property : Combine like terms: Subtract 72 from both sides: Use the quadratic formula to find solutions for : for In , assign:

• • • Solving, we get: Since the question stipulates that is positive, we have . Therefore, the two numbers are and .

Verify: Our two numbers are: Or, approximately 7.66 and 3.66.

Step-by-step explanation:

Let the two numbers be a and b.

One positive real number is four less than another. So, we can write that: The sum of the squares of the two numbers is 72. Therefore: Substitute: Solve for a. Expand: Simplify: Divide both sides by two: Subtract 36 from both sides: The equation isn’t factorable. So, we can use the quadratic formula: In this case, a = 1, b = -4, and c = -28. Substitute: Evaluate: So, our two solutions are: Since the two numbers are positive, we can ignore the second solution.

So, our first number is: And since the second number is four less, our second number is: 