Question

the sum of squares of two consecutive odd natural numbers is 290 find the numbers

Answer 1

Given : —

• sum of square of two consecutive odd natural numbers = 290

To find : —

• The numbers = ?

Solution : —

Let, x be the first number, then the second number will be (x + 2) .

According to the question : —

x² + (x + 2)² = 290

→ x² + x² + 2² + 2.x.2 = 290

→ 2x² + 4 + 4x = 290

→ 2(x² + 2 + 2x) = 290

→ (x² + 2 + 2x) = 290/2

→ x² + 2x + 2 = 145

→ x² + 2x + 2 - 145 = 0

→ x² + 2x - 143 = 0

→ x² + (13 - 11)x - 143 = 0

→ x² + 13x - 11x - 143 = 0

→ x(x + 13) - 11(x + 13) = 0

→ (x + 13) (x - 11) = 0

x + 13 = 0

→ x = - 13

x - 11 = 0

→ x = 11

★ Taking [ x = - 13 ]

→ ( x + 2 )

→ ( -13 + 2 )

→ -11

So, the numbers will be (-13) and (-11)

★ Taking [ x = 11 ]

→ ( x + 2 )

→ ( 11 + 2 )

→ 13

So, the numbers will be (13) and (11)