Question

A positive real number is 8 more than another. If the sum of the squares of the two numbers is 80, find the numbers

100

likes502 views

Darrell

4.5

61 Answers

Absolutely, let's solve this problem. Here's how to find the numbers:
**1. Set up the equations:**
* Let 'x' be the first number.
* The second number is 'x + 8' (since it's 8 more than the first).
* The sum of their squares is 80: x² + (x + 8)² = 80
**2. Solve the equation:**
* Expand the equation: x² + x² + 16x + 64 = 80
* Combine like terms: 2x² + 16x - 16 = 0
* Divide by 2 for simplicity: x² + 8x - 8 = 0
* Factor the quadratic equation: (x + 4)(x - 2) = 0
* Solve for possible values of x:
* x + 4 = 0 => x = -4 (We discard this since we need a positive real number)
* x - 2 = 0 => x = 2
**3. Find the second number:**
* Since x = 2, the second number is x + 8 = 2 + 8 = 10
**Answer:** The two numbers are 2 and 10.

Frequently asked questions (FAQs)

What is the derivative of the function f(x) = (10^x)/(e^x)?

+

Question: For the cosine function f(x) = cos x, what is the value of f(π/3)?

+

What is the maximum or minimum value of a quadratic function with vertex (2, -3)?

+

New questions in Mathematics