Among all pairs of numbers (x,y) such that 3x+y=8

tugmiddelc0

tugmiddelc0

Answered question

2021-11-16

Among all pairs of numbers (x,y)
such that
3x+y=8
find the pair for which the sum of squares, x2+y2
is minimum. Write your answers as fractions reduced to lowest terms

Answer & Explanation

Kevin Hunt

Kevin Hunt

Beginner2021-11-17Added 20 answers

3x+y=8
y=83x -(1)
Function to be minimum,
f=(x2+y2)
f=x2+(83x)2
f=x2+64+9x248x
f=10x248x+64


Critical point,
f=20x48
f=0
20x48=0
x=4820
x=125
fx)=20i.e.>0 so,
x=125 give minimum f.
y=83×125=40365=45
Answer is (x,y)=(125,45)

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