first we represent unknowns using variables,,
let x = first number
let x+2 = second number
note that since they are consecutive but both even numbers, the difference between them is 2, that's why the second number is x+2
now we set-up the equation,, since the sum of the squares (meaning both number are raised to 2) is equal to 340,
(x)^2 + (x+2)^2 = 340
x^2 + x^2 + 4x + 4 = 340
combine similar terms and simplify:
2x^2 + 4x + 4 - 340 = 0
2x^2 + 4x - 336 = 0
we can factor out 2 and cancel it:
2(x^2 + 2x - 168) = 0
x^2 + 2x - 168 = 0
since this quadratic equation is factorable,
(x + 14)(x - 12) = 0
x = -14 and x = 12
thus there are two pairs of answers:
(i) x = -14 and x+2 = -12
(ii) x = 12 and x+2 = 14
hope this helps~ :)
So the average of the two squares is 340/2=170.
What would you propose for the two consecutive even integers?
MATH - A four by four grid of unit squares contains squares of various sizes (1 ...
Math - Minimizing Sum: Find two positive numbers whose sum is 100 and the sum of...
Math - Two consecutive integers are squared. The sum of these squares of these ...
math - Find two positive numbers whose sum is 50 such that the sum of their ...
math - The difference of the cubes of two consecutive odd positive integers is ...
algebra - There are two-digit perfect squares whose square roots are the same as...
Math Word Problem - An area, A, consisting of the sum of two squares is 1000. ...
math - The sum of two numbers is 10.The sum of their squares is 52.Find the ...
Calculus - Find two numbers whose sum is 10 for which the sum of their squares ...
math - Two non-negative numbers are chosen such that their sum is 30. Find the ...