Hasil beserta caranya

7. Keempat bilangan membentuk barisan aritmatika,berarti
p = a
q = a + b
r = a + 2b
s = a + 3b
p.s = 46
q.r = 144
a(a + 3b) = 46
a² + 3ab = 46
3ab = 46 - a²
b = 1/3((46-a²)/a))
(a + b)(a + 2b) = 144
(a + 1/3((46-a²)/a)(a + 2/3((46-a²)/a) = 144
((3a² + 46 - a²)/3a)((3a² + 2(46 - a²))/3a) = 144
(2a² + 46)(a² + 92)/9a² = 144 (kali 9a²)
(2a⁴ + 184a² + 46a² + 4232) = 1296a²
2a⁴ - 1066a² + 4232 = 0 (bagi 2)
a⁴ - 533a² + 2116 = 0
(a² - 529)(a² - 4) = 0
a = √529 = 23 atau
a = √4 = 2
Karena yang diminta positif, maka a = 2.
3ab = 46 - a²
3(2)b = 46 - 2²
6b = 42
b = 7
S4 = 4/2(2(2) + (4 - 1)(7)) = 2(4 + 21) = 25 x 2 = 50
Maaf, jika hasilnya lumayan panjang.