Question

Ada yg tau cara nyari nilai minimum ini?

jika 5x + 12y = 60 maka nilai minimum akar x kuadrat + y kuadrat adalah?

Answer 1

5x + 12y = 60
5x = 60-12y
x = 12-12y/5
p = √x²+y²  = √(12-12y/5)²+y²  = √144-2.144y/5+144y²/25 + 25y²/25
=√144-288y/5 + 169y²/25

Pmin jika P ' = 0
P ' = 1/2 (-288/5+ 2.169y/25) / (√144-288y/5 + 169y²/25) = 0
pembilang harus 0

-288/5+ 2.169y/25 = 0
2.169y/25 = 288/5
169y=144. 5
y=144 . 5 /169

x = 12-12y/5  = 12 - 12. 144. 5 / 5. 169 = 12 - 12.144/169
=(12.169-12.144)/169 = 12(169-144) / 169  = 12. 25 / 169


p = √x²+y² = √12² . 25² / 169²  + 144².5²/169²  = 1/169 √12².25²+144².5²
1/169√144.25(25+144) = 1/169 . ( 12.5) √169 = 13/169 . 60 = 60/13

jawaban A