Question

Two consecutive positive even numbers the sum of whose square is 340​

Answer 1

Step-by-step explanation:

let the numbers be X and X+2 then

( X) ^2 + ( X+2) ^2 = 452

x^2 + x^2 +4+ 4x= 452

2 x^2 + 4x - 448 = 0

x^2 + 2x - 224 = 0

x^2 + 16x -14x -224 = 0

X( X+16) - 14( X+16)= 0

( X+16)(X-14) =0

X = 14,-16

the numbers are either 14 and 16 or -16 and -14

Answer 2

let the two consecutive positive even numbers be x,x+2

x^2+(x+2)^2=340

x^2+x^2+4+4x=340

2x^2+4x=336

2(x^2+2x-168)=0

x^2+2x-168=0

x^2+14x-12x-168=0

x(x+14)-12(x+14)=0

Therefore,x=12,-14