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Question
Complete the following activity to solve the given word problem. The Sum of squares of two consecutive even natural numbers is 244, then find those numbers.
Activity: Let the first even natural number be x
Therefore its consecutive even natural number will be = (______)
By the given condition,
x2 + (x + 2)2 = 244
x2 + x2 + 4x + 4 – (______) = 0
2x2 + 4x – 240 = 0
x2 + 2x – 120 = 0
x2 + (______) – (______) – 120 = 0
x(x + 12) – (______) (x + 12) = 0
(x + 12)(x – 10) = 0
x = (______)/x = 10
But natural number cannot be negative, x = – 12 is not possible.
Therefore first even natural number is x = 10.
Second even consecutive natural number = x + 2 = 10 + 2 = 12.
Solution
Let the first even natural number be x.
Therefore its consecutive even natural number will be = (x + 2)
By the given condition,
x2 + (x + 2)2 = 244
x2 + x2 + 4x + 4 – 244 = 0
2x2 + 4x – 240 = 0
x2 + 2x – 120 = 0 ........[Dividing both sides by 2]
x2 + 12x – 10x – 120 = 0
x(x + 12) – 10 (x + 12) = 0
(x + 12)(x – 10) = 0
x + 12 = 0 or x - 10 = 0
x = -12/x = 10
But natural number cannot be negative, x = – 12 is not possible.
Therefore first even natural number is x = 10.
Second even consecutive natural number = x + 2 = 10 + 2 = 12.
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