Question

Find three consecutive even numbers if it is known that the sum of the squares of the first 2 is equal to the square of the third number.

Answer 1

To find three consecutive even numbers, let the first number be 'x'. The second consecutive even number would then be 'x+2', and the third consecutive even number would be 'x+4'. Solve the equation and you will find the consecutive even numbers.

Step-by-step explanation:

To find three consecutive even numbers, we can let the first number be 'x'. The second consecutive even number would then be 'x+2', and the third consecutive even number would be 'x+4'. We know that the sum of the squares of the first two numbers is equal to the square of the third number, so we can set up the following equation:

x^2 + (x+2)^2 = (x+4)^2

Expanding and simplifying the equation, we get:

x^2 + x^2 + 4x + 4 = x^2 + 8x + 16

Combining like terms and simplifying further, we get:

x^2 - 4x - 12 = 0

Factoring and solving for 'x', we find that 'x = 6' or 'x = -2'.

Therefore, the consecutive even numbers are 6, 8, and 10.

Answer 2

`(2n)^2+(2n+2)^2=(2n+4)^2\\ 4n^2+4n^2+8n+4=4n^2+16n+16\\ 4n^2-8n-12=0\\ 4(n^2-2n-3)=0\\ n^2-2n-3=0\\ n^2+n-3n-3=0\\ n(n+1)-3(n+1)=0\\ (n-3)(n+1)=0\\ n=3 \vee n=-1\\\\ \underline{n=3}\\ 2n=6\\ 2n+2=8\\ 2n+4=10\\\\ \underline{n=-1}\\ 2n=-2\\ 2n+2=0\\ 2n+4=2`

6,8,10 or -2,0,2