Question

sum of the squares of two consecutive even numbers is 452.a)if one number is 'x'what is the next number? b) form the second degree equation and find the numbers.
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Answer 1

Answer:

14 and 16

Step-by-step explanation:

Let the smaller number be x. Since both the numbers are even, then the next number should be x + 2. ( since x + 1 represents an odd number if x is even ).

According to the question:  

⇒ Sum of squares of those numbers = 452

⇒ x^2 + ( x + 2 )^2 = 452

⇒ x^2 + x^2 + ( 2 )^2 + 2( 2 )( x ) = 452

⇒ 2x^2 + 4 + 4x = 452

⇒ 2x^2 + 4x + 4 - 452 = 0

⇒ 2x^2 + 4x - 248 = 0

⇒ x^2 + 2x - 124 = 0         [ Equation formed ]

⇒ x^2 + ( 16 - 14 )x - 124 = 0

⇒ x^2 + 16x - 14x - 124 = 0

⇒ x( x + 16 ) - 14( x + 16 ) = 0

⇒ ( x + 16 )( x - 14 ) = 0

Using zero product rule ; x + 16 = 0

                                   Or x - 14 = 0

x = - 16 or x = 14

Since x = 14, for positive numbers,

x + 2 = 14 +2 = 16

Hence the required numbers are 14 and 16.