Question

Find the two consecutive even integers whose square have the sum 340

Answer 1

Answer:

The numbers are 12 and 14

Step-by-step explanation:

To find the answer, setup an equation

set 'x' equal to the lower, and x+2 as the higher number since they are consecutive even numbers so they are two apart

Now write out the equation according to the question

(x)²+(x+2)²=340

x²+x²+4x+4=340

combine like terms

2x²+4x+4=340

set equal to zero so you can factor

2x²+4x-336=0

(2x+28)(x-12)=0

x= -14,12

x=12because the answer must be positive according to the question

That means x+2 is 14

you can double check:

(12)²+(14)²=340

144+196=340

340=340

Answer 2

Answer:

Let the two consecutive even numbers be 2x and 2x+2.

Now,

(x)²+(x+2)²=340

x²+x²+4x+4=340

2x²+4x=340-4

x²+4x=336

x²+4x-336=0

Factorise the equation

(2x+28)(x-12)=0

x=14 and x=12