Sum of squares of four consecutive even numbers is 504. Find the average of four numbers?

Subject:
Math
Author:
kailee
Created:
1 year ago

Answers 2

Answer:

126

Step-by-step explanation:

average =sum of the squares of consecutive/total number of consecutive

e.i 504/4=126

Author:

ryan701
Rate an answer:
4

[tex]\large\underline{\sf{Solution-}}[/tex]

Let assume that,

Four consecutive even numbers be x, x + 2, x + 4, x + 6.

According to statement,

Sum of squares of four consecutive even numbers is 504.

So,

[tex]\sf \: {x}^{2} + {(x + 2)}^{2} + {(x + 4)}^{2} + {(x + 6)}^{2} = 504 \\ \\ [/tex]

[tex]\sf \: {x}^{2} + {x}^{2} + 4 + 4x + {x}^{2} + 16 + 8x + {x}^{2} + 36 + 12x = 504 \\ \\ [/tex]

[tex]\sf \: 4{x}^{2} + 24x + 56= 504 \\ \\ [/tex]

[tex]\sf \: 4{x}^{2} + 24x + 56 - 504 = 0 \\ \\ [/tex]

[tex]\sf \: 4{x}^{2} + 24x - 448 = 0 \\ \\ [/tex]

[tex]\sf \: 4({x}^{2} + 6x - 112) = 0 \\ \\ [/tex]

[tex]\sf \: {x}^{2} + 6x - 112 = 0 \\ \\ [/tex]

[tex]\sf \: {x}^{2} + 14x - 8x - 112 = 0 \\ \\ [/tex]

[tex]\sf \: x(x + 14) - 8(x + 14) = 0 \\ \\ [/tex]

[tex]\sf \: (x + 14) (x - 8) = 0 \\ \\ [/tex]

[tex]\bf\implies \:x = - 14 \: \: \: or \: \: \: x = 8 \\ \\ [/tex]

So,

Numbers are 8, 10, 12, 14

Numbers are - 14, -12, - 10, - 8

So,

[tex]\bf \: Average = \dfrac{8 + 10 + 12 + 14}{4} = \dfrac{44}{4} = 11\\ \\ [/tex]

[tex]\bf \: Average = \dfrac{ - 8 - 10 - 12 - 14}{4} = \dfrac{ - 44}{4} = - 11\\ \\ [/tex]

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billyjsgv
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Sum of squares of four consecutive even numbers is 504. Find the average of four numbers?​

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Sum of squares of four consecutive even numbers is 504. Find the average of four numbers?