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There are two consecutive odd integers whose sum is 340. They are 169 and 171.
The sum of the squares of two consecutive positive even integers is 340. Find the integers.
There are no such integers. Proof: choose any positive whole number x two consecutive even integers: (2x) (2x+2) Take the sum (2x)+(2x+2) (2x)+(2x+2)=340 4x+2=340 4x=338 x=338/4=84.5 Since this is not a whole number, there is no whole number that satisfies the conditions. (There are two consecutive odd integers which add up to 340: 169 and 171)
Let the number be 'm' & 'm + 2' Hence their squares are m^2 & (m+2)^2 There sum is m^2 + (m+2)^2 = 340 Multiply out he brackets m^2 + m^2 + 4m + 4 = 340 . 2m^2 + 4m + 4 = 340 Divide both sides by '2' m^2 + 2m + 2 = 170 m^2 + 2m - 168 = 0 Factor (m - 12)(m + 14) = 0 Hence m = 12 & m+ 2 = 14 The two consecutive even numbers. 12^2 = 144 14^2 = 196 144 + 196 = 340 As required.
YES!!!! Any number that ends/terminates in 0,2,4,6,or 8. is an even number. Hence 340 ends in '0' so it is even. 1,000,000 (One million) is even , it ends in '0' 1,000,001 is ODD as it does not end in 0,2,4,6, or 8.