Question

If xy = 144, x + y = 30, and x > y, what is the value of x – y ?

F. 4
G. 6
H. 18
J. 22
K. 24

Answer 1

`xy=144\\x+y=30\to x=30-y\\\\substitute:\\\\(30-y)y=144\\-y^2+30y-144=0\\\\\Delta=30^2-4\cdot(-1)\cdot(-144)=900-576=324;\ \sqrt\Delta=√(324)=18\\\\y_1=(-30-18)/(2\cdot(-1))=(-48)/(-2)=24;\ y_2=(-30+18)/(2\cdot(-1))=(-12)/(-2)=6\\\\x_1=30-24=6;\ x_2=30-6=24\\\\x > y\ to x=24\ and\ y=6\\\\x-y=24-6=18\\\\Answer:H.`