Question

The sum of square of two consective even integers is 340. Find the number​

Answer 1

Answer:

12 and 14.

Step-by-step explanation:

when we add square of these two numbers,

then 12×12+14×14=

144+196 =340.

so the consecutive even numbers are 12 and 14.

I hope it will helps you.

if it is right then mark as brainlist...please

Answer 2

$\bf\huge\underline{Answer :-}$

Given :

• Sum of the square of two consecutive even integers = 340

To find :

• The two numbers

Solution :

Let the two positive integers be 'x' & 'x + 2'

According to question,

$\sf\longrightarrow {x}^{2} + {(x+2)}^{2} = 340$

$\sf\longrightarrow {x}^{2} + x(x + 2) + 2(x + 2) = 340$

$\sf\longrightarrow {x}^{2} + {x}^{2} + 2x + 2x + 4 = 340$

$\sf\longrightarrow {2x}^{2} + 4x + 4 = 340$

$\sf\longrightarrow {2x}^{2} + 4x = 340 - 4$

$\sf\longrightarrow {2x}^{2} + 4x = 336$

$\sf\longrightarrow 2 ({x}^{2} + 2x) = 336$

$\sf\longrightarrow {x}^{2} + 2x = \dfrac{336}{2}$

$\sf\longrightarrow {x}^{2} + 2x = 168$

$\sf\longrightarrow {x}^{2} + 2x - 168 = 0$

$\sf\longrightarrow {x}^{2} + (14x - 12x) - 168 = 0$

$\sf\longrightarrow {x}^{2} + 14x - 12x - 168 = 0$

$\sf\longrightarrow x(x + 14) - 12(x + 14) = 0$

$\sf\longrightarrow (x - 12) (x + 14) = 0$

$\sf\therefore Either, x - 12 = 0 \: \: or, (x + 14) = 0$

$\sf\longrightarrow x = 12 \: \: \: or, x = -14 (Neglected)$

$\longrightarrow\boxed{\underline{\sf \therefore x = 12}}$

$\underline{\sf \star Hence, \: the \: first \: integer \: = \: 12}$

$\underline {\sf and \: the \: second \: integer \: = \: 14}$