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.

Answer 1

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.