Question

The sum of the squares of two consecutive odd number is 394.The mathematics equation for The above statement is....​

Answer 1

Answer:

So if one number is 'x' then the other consecutive odd number can be found by adding 2 to the 1stnumber. So let us take 2 consecutive odd numbers as x and x + 2. Now it is given that the sum of squares of these consecutive numbers x and (x + 2) is 394. We know, (a+b)2=a2+2ab+b2.

Answer 2

Answer:

let the two consecutive odd numbers be x,x+2

squares are x²,(x+2)²

sum of them is 394

${x}^{2} + {(x + 2)}^{2} = 394 \\ {x}^{2} + {x}^{2} + 4 + 4x = 394 \\ 2 {x}^{2} + 4x + 4 = 394 \\ 2( {x}^{2} + 2x + 2) = 394 \\ {x}^{2} + 2x + 2 = 394 \div 2 \\ {x}^{2} + 2x + 2 = 197 \\ {x}^{2} + 2x =195 \\ {x}^{2} + 2x - 195 = 0 \\ {x}^{2} + 15x - 13x - 195 = 0 \\ x(x + 15) - 13(x + 15) = 0 \\ (x + 15)(x - 13) = 0 \\ x = 13 \\ x = - 15$

so the odd numbers are 13,15

or -15,-13