Helping students gain understanding and self-confidence in algebra.
Motherof8 wrote:The sum of 2 numbers is 20 and the sum of their squares is 202. Find the numbers. I can't seem to find any numbers that add up to 20 whose squared add up to 202. I've tried all the numbers but they all come out as more than 202. I've even tied some negative numbers and whole numbers with fractions. What am I missing?
Motherof8 wrote:I guess the equation would be x +y -20=0 and x squared + Y squared -202 = 0. I didn't know exactly how to solve an equation with regular variables and those that are squared, so I just plugged in certain values for the variables to see if they worked. 10 + 10 =20. 100 + 100 = 200, not 202. 4x 4 = 16, and 16 x 16 is 256, which is more than 202.13 squared is 169 and 7 squared is 49, which adds up to 218 which is more than 202. 12 squared is 144, and 8 squared is 64, which still add up to 208, more than 202. Negative numbers squared are positive, so that wouldn't work.
Motherof8 wrote:I didn't know exactly how to solve an equation with regular variables and those that are squared...
Motherof8 wrote:If one divides the variables, one comes up with x and y.
Motherof8 wrote:20 -x squared is 400 -40x + 2x squared.