Question

Sum of the squares of two positive consecutive even numbers is 1060 what is the smaller number

Answer 1

Hi Mate !!


Let the First consecutive no. be x
then 2nd will be x + 2 bcoz , it is given that the nos. are even consecutive no.

• Their Sum is 1060

x² + ( x + 2 )² = 1060

[ Using identity :- ( a + b )² = a² + 2ab + b² ]

x² + x² + 4 + 4x = 1060

2x² + 4x = 1060 - 4

2x² + 4x = 1056

2x² + 4x - 1056 = 0

{ dividing both side by 2 }

x² + 2x - 528 = 0

x² + 24x - 22x - 528 = 0

x ( x + 24 ) - 22 ( x + 528 ) = 0

( x + 24 ) ( x - 22 ) = 0


° ( x + 24 ) = 0

x = -24 .... [ Neglected bcoz , it is given in question that the nos. are positive ]


° ( x - 22 ) = 0

x = 22


So, the 1st no. is x = 22 ( smallest no. )
and 2nd no. is ( x + 2 ) = 24


So, the smallest no. is 22 !!

Answer 2

22 is the ans........