Question

the product of two integers is -24, and the sum of the squares of these two integer is 73. what are the two integer? help me solve this please

Answer 1

x.y=-24--- This gives y=-24/x , y^2=576/x^2
x^2+y^2=73
Now replace y^2 using above y^2=576/x^2\[x^{2}+576/x^{2}=73\]
\[x ^{4}+576=73x^{2}\]\[x^{4}-73x^{2}+576=0\]
Now let us assume x^2=a
x^4=a^2
\[a ^{2}-73a+576=0\]
factors of 576 9*64\[(a-9)(a-64)=0\]
\[a=9;a=64\]
replace a with x^2\[x^{2}=9;x^{2}=64\]
\[x=+3,-3,+8,-8\]
correspondingly
y=-24/x=-8,+8,-3,+3

therefore,
-3,8 or +3,-8 is your solution

Answer 2

(x,y)={(-8,3),(-3,8),(3,-8),(8,-3)}
Simply...the two integers can be 8 and -3 or -8 and 3