SOLUTION: Among all pairs of numbers (x,y) such as 4x+y=17 find the pair of which the sum o squares x^2+y^2 is minimum. Write the answer as reduced fractions.
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Question 1019565: Among all pairs of numbers (x,y) such as 4x+y=17 find the pair of which the sum o squares x^2+y^2 is minimum. Write the answer as reduced fractions. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Among all pairs of numbers (x,y) such as 4x+y=17 find the pair of which the sum o squares x^2+y^2 is minimum.
Write the answer as reduced fractions.
:
convert the equation to the slope intercept form
y = -4x + 17
:
x^2 + y^2
replace y with (-4x+17), put in the form of an equation
f(x) = x^2 + (-4x+17)^2
:
FOIL (-4x+17)(-4x+17)
f(x) = x^2 + 16x^2 - 68x - 68x + 289
Combine like terms
f(x) = 17x^2 - 136x + 289
The minimum occurs at the axis of symmetry; x = -b/(2a), where a=17, b=-136
x =
x =
x = 4
Find y
y = -4(4) + 17
y = -16 + 17
y = 1
:
x^2 + y^2 minimum; x=4, y=1 or x=1, y=4
