Answer to Question #145824 in Algebra for Yui

Question

The sum of two numbers is 13, and the sum of their squares is 89. If x is the

first number. Find this number.

Answer 1

if x is the first number then (13-x) is the second one

So, sum of their squares is 89; x²+(13-x)²=89; x²+169- 26x+x²=89; 2x²-26x+80=0;

x² -13x+40=0;

D=169-160=9;

x₁=(13+3)/2=8;

x₂=(13-3)/2=5.

checkup: 8+5=13; 64+25=89

So x can be either 5 or 8 .