Two integers differ by 12 and the sum of their squares is 74. Find the integers.
The answers are : -7 and 5 or 7 and -5.
Could you please show me how to work this problem out?
Two integers differ by 12 and the sum of their squares is 74. Find the integers.
The answers are : -7 and 5 or 7 and -5.
Could you please show me how to work this problem out?
Hello Tessarina$\displaystyle (y+12)^2+y^2=74$
$\displaystyle \Rightarrow y^2+24y+144+y^2=74$
$\displaystyle \Rightarrow 2y^2+24y +70=0$
$\displaystyle \Rightarrow y^2+12y+35=0$
$\displaystyle \Rightarrow (y+5)(y+7)=0$
$\displaystyle \Rightarrow y = -5, -7$
$\displaystyle \Rightarrow x = y+12 = 7, 5$
So the solutions are $\displaystyle (7, -5)$ and $\displaystyle (5, -7)$.
Grandad