Question

sum of the squares of two consecutive positive even integers is hundred find those numbers by using quadratic equations​

Answer 1

Let the numbers be x and x+1.

AQ,

Let's define them as  

X and X+2

 

From the first sentence we know

 

X2 + (X+2)2 = 100

 

Expanding this we have

 

X2 + (X2+4X+4) = 100

2X2 + 4X + 4 = 100

2X2 + 4X + 4 -100 = 0

2X2 + 4X - 96 = 0

 

Divide by 2

x2 + 2x - 48 = 0

 

And factor

(x+8)(x-6) = 0

 

Set each factor equal to 0 and solve for X.

 

X + 8 = 0    X = -8

X - 6 = 0     X = 6

 

We need to check these two solutions and see if they meet the initial condition.

 

if X=-8, then we have

 

(-8)2 + (-8+2)2 = 64+(-6)2 = 64+36=100

 

if X=6, then we have

(6)2 + (6+2)2 = 36+(8)2 = 36+64=100

 

Both solutions work.

 

So the integers are 6 & 8 OR -8 & -6.