Answer:
12, 14 are two consecutive positive even numbers
Step-by-step explanation:
Let x, x+2 are two consecutive positive even numbers
According to given Condition
[tex]x^{2} + (x+2)^{2} = 340[/tex]
[tex]x^{2} +x^{2} + 4 + 4x = 340[/tex]
[tex]2x^{2} + 4 + 4x - 340 = 0[/tex]
[tex]2x^{2} + 4x - 336 = 0[/tex]
[tex]2x^{2} +28x -24x - 336 = 0[/tex]
[tex](2x^{2} +28x) -(24x + 336) = 0[/tex]
[tex]2x(x} +14) - 24(x + 14) = 0[/tex]
[tex](2x -24) (x + 14) = 0[/tex]
[tex]2x - 24 = 0[/tex] or [tex]x+14 = 0[/tex]
[tex]x = \frac{24}{2} = 12[/tex] or [tex]x = -14[/tex]
As Number is positive so x = 12
x+ 2= 14
12, 14 are two consecutive positive even numbers
21 and 22 are two consecutive numbers whose squares, when subtracted, equals 43.
