The sum of two numbers is 8, and the sum of their squares is 34. what is the larger number

The larger number is 5.

Step-by-step explanation:

Let the numbers be represented by x and y.  Then:

x + y = 8   is their sum, and

x² + y² = 34 is the sum of their squares.

Let's solve this system of equations using substitution.  Since x + y = 8,

x = 8 - y.  Subbing this 8 - y for x into the second equation, we get:

(8 - y)² + y² = 34, or

64 - 16 y + y² + y² = 34

Simplifying, we get first: 30 - 16y + 2y² = 0, and then:

2y² - 16y + 30 = 0, and after reducing, y² - 8y + 15 = 0.

This factors into (y - 3)(y - 5) = 0, and so y = 3 and y = 5.

The larger number is 5.

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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