In the given problem, you need to apply your knowledge and skills in alegbra and basic math especially in identify unknown variables.
x is the smaller number
y is the other number
"sum of two integers is 15"
→ x + y = 15, first equation
"sum of their squares is at most 170"
→ x² + y² < 170, second equation
x + y = 15 → x = 15 - y
x² + y² < 170
(15-y)² + y² < 170
225 - 30y + y² + y² < 170
225 - 30y + 2y² < 170
2y² - 30y + 55 < 0
y² - 15y + 27.5 < 0
y² - 15y + 56.25 < 56.25 - 27.5
(y-7.5)² < 28.75
y-7.5 < ± 5.36
y < 12.86, y < 2.14
2.14 > y < 12.86
x+y = 15
for y < 2.14
x + 2.14 = 15
x = 12.86
for y < 12.86
x + 12.86 = 15
x = 2.14
2.14 < x < 12.86
Pair of Numbers
(2.14, 12.86), (2.13, 12.85), (2.12, 12.84), ..., (12.86, 2.14)
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Answers & Comments
Verified answer
In the given problem, you need to apply your knowledge and skills in alegbra and basic math especially in identify unknown variables.
Let:
x is the smaller number
y is the other number
Step 1: Create equation based from the Statement given.
"sum of two integers is 15"
→ x + y = 15, first equation
"sum of their squares is at most 170"
→ x² + y² < 170, second equation
Step 2: Substitute the first equation to the 2nd equation.
x + y = 15 → x = 15 - y
x² + y² < 170
(15-y)² + y² < 170
225 - 30y + y² + y² < 170
225 - 30y + 2y² < 170
2y² - 30y + 55 < 0
y² - 15y + 27.5 < 0
Use completing the square
y² - 15y + 56.25 < 56.25 - 27.5
(y-7.5)² < 28.75
y-7.5 < ± 5.36
y < 12.86, y < 2.14
2.14 > y < 12.86
Find the value of x
x+y = 15
for y < 2.14
x + 2.14 = 15
x = 12.86
for y < 12.86
x+y = 15
x + 12.86 = 15
x = 2.14
2.14 < x < 12.86
Final Answer:
Pair of Numbers
(2.14, 12.86), (2.13, 12.85), (2.12, 12.84), ..., (12.86, 2.14)
Learn more about solving unknown variables here at, brainly.ph/question/4917746
#CarryOnLearning
#BRAINLYFAST