Question

Find two consecutive odd natural numbers sum of whose squares is 130

Answer 1

let , x and (x + 2 ) are those consecutive odd natural numbers.
according to question

given , sum of squares = 130

x^2 + ( x + 2 )^2 = 130

x^2 + x^2 + 4x + 4=130

2x^2 + 4x=126

2(x^2 + 2x ) = 126

x^2 + 2x = 63

x^2 + 2x - 63 = 0

x^2 + 9x - 7x - 63 = 0

x( x + 9 ) -7 ( x + 9 )= 0

(x - 7 ) (x + 9 ) = 0

x - 7=0 , x + 9 =0

x = 7 , x = - 9

natural numbers can not be considered as negative. so take positive value of 'x'

now the required numbers are

x =7 , x + 2 = 7 + 2= 9

therefore , the required consecutive odd natural numbers sum of whose squares is 130 are 7 and 9.
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Your Answer : 7 , 9
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Answer 2

Answer:

The numbers are 9 and 7.