Two positive numbers differ by 5 and the sum of their squares is 193 . find the two numbers
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Answered by
3
Answer:
Let the two positive whole numbers be x and y.
Given that these numbers differ by = 5
Therefore x - y = 5
x = 5 + y
Also given that the sum of their squares = 193
Therefore
x² + y² = 193
Substituting the value of x
(5 + y)² + y² = 193
25 + y² + 10y + y ² = 193
2y² + 10y - 168 = 0
y² + 5y - 84 = 0
y² + 12y - 7y - 84 = 0
y(y + 12) - 7(y + 12)
(y + 12) (y - 7) = 0
y = -12 or y = 7
Rejecting y = -12 as given they are positive whole numbers.
Therefore y = 7
x - 7 = 5
x = 12
The two numbers are 12 and 7.
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Answered by
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The two numbers are 7 and 12.
Step-by-step explanation:
Let x and y be the two numbers.
Then it is given that x = y + 5 ------------(1)
x² + y² = 193 -------------(2)
Substituting (1) in (2), we get:
(y + 5)² + y² = 193
25 + y² + 10y + y ² = 193
2y² + 10y - 168 = 0
Let's solve the quadratic equation.
y² + 5y - 84 = 0
y² + 12y - 7y - 84 = 0
y (y + 12) - 7(y + 12)
(y + 12) (y - 7) = 0
Therefore y = -12 or +7
It is mentioned that the numbers are positive whole numbers. So y can only be +7.
Substituting y = 7 in equation 1, we get: x = 12
So the two numbers are 7 and 12.
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