the difference between two numbers is 2 and the sum of their squares is 52. find the numbers
this is a problem solving using rational expressions.
Answers
Answered by
1
Answer: 25 and 27
Step-by-step explanation:
Answered by
8
Answer:
Let x and y be the two unknown numbers. Since you have two unknowns, you need two equations to solve for them:
The difference between two numbers is 2: x-y = 2
The sum of their squares is 52: x2 + y2 = 52
Since x-y=2, then x = 2+y. Substitute 2+y in place of x in the second equation then solve it for y:
x2 + y2 = 52
(2+y)2 + y2 = 52
y2 + 4y + 4 + y2 = 52
2y2 + 4y - 48 = 0
Divide both sides by 2:
y2 + 2y - 24 = 0
Factors to:
(y+6)(y-4) = 0
y = -6 and 4
x = 2+y
x = 2+-6 = -4
x = 2+4=6
There are two sets of numbers that satisfy the condition: (-6, -4) and (4, 6)
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