Question
Download Solution PDFWhat is the sum of two consecutive even numbers, the difference of whose squares is 84?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The sum of two consecutive even numbers is to be calculated where the difference of their squares is 84.
Formula Used:
Difference of squares = (a + b)(a - b)
Sum of two consecutive even numbers = a + b
Calculation:
Let the two consecutive even numbers be a and b.
Since they are consecutive even numbers, a = b - 2.
Difference of squares = 84
(b2 - a2) = 84
⇒ (b + a)(b - a) = 84
Substitute a = b - 2:
⇒ (b + (b - 2))(b - (b - 2)) = 84
⇒ (b + b - 2)(2) = 84
⇒ (2b - 2)(2) = 84
⇒ 4b - 4 = 84
⇒ 4b = 88
⇒ b = 22
Substitute b = 22 to find a:
a = b - 2
a = 22 - 2
a = 20
Sum of a and b:
⇒ a + b = 20 + 22 = 42
The sum of two consecutive even numbers is 42.
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