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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

Sagot :

[tex]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=\sqrt{324}=18\\\\y_1=\frac{-30-18}{2\cdot(-1)}=\frac{-48}{-2}=24;\ y_2=\frac{-30+18}{2\cdot(-1)}=\frac{-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.[/tex]
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