A dan B adalah bilangan rill, sehingga a+b = 1per a + 1per b = √39. Nilai a per b + b per a + 1980 adalah?.

a + b = √39

1/a + 1/b = √39
(a + b)/(ab) = √39
√39 / (ab) = √39
ab = 1

a/b + b/a + 1980
= (a^2 + b^2)/(ab) + 1980
= ((a + b)^2 - 2ab)/(ab) + 1980
= (√39^2 - 2(1))/1 + 1980
= 39 - 2 + 1980
= 2017

● Dik : a + b = 1/a + 1/b = √39
→ a + b = √39
→ 1/a + 1/b = b + a / ab = √39
. → b + a = √39 , dan ab = 1

● Dit : a/b + b/a + 1980 = .. ?

→ a/b + b/a = a² + b² / b.a

(a + b)² = a² + 2ab + b²
(a + b)² - 2ab = a² + b²
(√39)² - 2(1) = a² + b²
39 - 2 = a² + b²
a² + b² = 37

= a/b + b/a + 1980
= [(a² + b²) / ab] + 1980
= [37 / 1] + 1980
= 37 + 1980
= 2017