Question

Express 441 square number as the sum of two consecutive natural numbers

Answer 1

Answer:

14² + 15² = 421

15² + 16² = 481

Step-by-step explanation:

Express 441 square number as the sum of two consecutive natural numbers

Let say two consecutive natural numbers are

n  & n+1

n² + (n+1)² = 441

=> n² + n² + 1 + 2n = 441

=> 2n² + 2n - 440 = 0

dividing by 2 both sides

=> n² + n - 220 = 0

There are no proper factor

So question can be either 421  or 481

lets take first 421

then

n² + n² + 1 + 2n = 421

=> 2n² + 2n - 420 = 0

dividing by 2 both sides

=> n² + n - 210 = 0

=> n² + 15n - 14n - 210 = 0

=> n(n+15)-14(n+15) = 0

=> (n-14)(n+15) = 0

n = 14    n = -15 (-ve integer not possible)

n+1 = 15

14² + 15² = 421

Similarly taking 481

n² + n² + 1 + 2n = 481

=> 2n² + 2n - 480 = 0

dividing by 2 both sides

=> n² + n - 240 = 0

=> n² + 16n - 15n - 210 = 0

=> n(n+16)-15(n+16) = 0

=> (n-15)(n+16) = 0

n = 15    n = -16 (-ve integer not possible)

n+1 = 16

15² + 16² = 481

Answer 2

Answer:

Step-by-step explanation:

Let x and x + 1 be 2 consecutive natural numbers.Now, x + x + 1 = 212⇒2x + 1 = 441⇒2x = 440⇒x = 220Now, first number = 220second number = 220 + 1 = 221So, consecutive natural numbers are : 220 and 221Let x and x + 1 be 2 consecutive natural numbers.Now, x + x + 1 = 212⇒2x + 1 = 441⇒2x = 440⇒x = 220Now, first number = 220second number = 220 + 1 = 221So, consecutive natural numbers are : 220 and 221

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