The sum of two numbers is 20 and the difference between their squares is 80. Select the two numbers from the given options.
Given:
Sum of two numbers = 20
Difference between their squares = 80
Concept Used:
Algebraic identities: a² - b² = (a + b)(a - b)
Solution:
Let the two numbers be 'a' and 'b'.
a + b = 20 .... (1)
a² - b² = 80
80 = (20)(a - b)
a - b = 4 .....(2)
Adding the two equations:
2a = 24
a = 12
Substituting the value of 'a' in the first equation:
12 + b = 20
b = 20 - 12
b = 8
The two numbers are 12 and 8.
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