Question

what is the sum of two consecutive even number the difference of whose squares is 84 ​

Answer 1

The sum of two consecutive even number the difference of whose squares is 84 is 42

Given :

For two consecutive even number the difference of whose squares is 84

To find :

Find the sum of two consecutive even number

Solution :

Step 1 of 2 :

Form the equation to find the sum

Let the two consecutive even numbers are x and x + 2

By the given condition

$\displaystyle \sf{ {(x + 2)}^{2} - {x}^{2} = 84}$

Step 2 of 2 :

Find the sum

$\displaystyle \sf{ {(x + 2)}^{2} - {x}^{2} = 84}$

$\displaystyle \sf{ \implies {x}^{2} + 4x + 4 - {x}^{2} = 84 }$

$\displaystyle \sf{ \implies 4x + 4 = 84 }$

$\displaystyle \sf{ \implies 4x = 80 }$

$\displaystyle \sf{ \implies x = \frac{80}{4} }$

$\displaystyle \sf{ \implies x = 20 }$

So two consecutive even numbers are 20 and 22

Hence the sum of two consecutive even numbers

= 20 + 22

= 42

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Answer 2

Step-by-step explanation:

Noting is here !

just we need to hold the number x and x+2....

then by applying a²+b² formula i.e (a+b) (a-b) ....

and then adding the consecutive number....

our sum is completed

please support me.....