Mathematics
The sum of two numbers is 8 and the difference of their squares is 32. Find the numbers.
Linear Equations
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Answer
Let two numbers be x and y, such that x > y.
Given,
Sum of two numbers = 8
⇒ x + y = 8
⇒ x = 8 - y ……..(1)
Given,
Difference of squares = 32
⇒ x2 - y2 = 32
⇒ (8 - y)2 - y2 = 32
⇒ 82 + y2 - 2 × 8 × y - y2 = 32
⇒ 64 - 16y = 32
⇒ 16y = 64 - 32
⇒ 16y = 32
⇒ y = = 2.
Substituting value of y in equation (1), we get :
⇒ x = 8 - 2 = 6.
Hence, numbers are 2 and 6.
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