jika a dan b adalah akar persamaan kuadrat x^2-3x-1 maka a^4+6a^2b^2+b^4=

x² - 3x - 1 ; diperoleh p = 1, q = -3, r =-1

a + b= -q/p = -(-3)/1 = 3
a.b = c/p = -1/1 = -1

a⁴ + 6a²b² + b⁴
= (a + b)⁴ - 4a³b - 4ab³
= (a + b)⁴ - 4ab(a² + b²)
= (a + b)⁴ - 4ab((a + b)² - 2ab)
= (3)⁴ - 4(-1)((3)² - 2(-1))  
= 81 + 4(9 + 2)
= 81 + 44
= 125

cmiiw

x^2 - 3x - 1 = 0
a + b = -(-3)/1 = 3
ab = -1/1 = -1

a^2 + b^2 = (a + b)^2 - 2ab = (3)^2 - 2(-1) = 9 + 2 = 11

a^4 + 6a^2b^2 + b^4
= a^4 + 2a^2b^2 + b^4 + 4a^2b^2
= (a^2 + b^2)^2 + 4(ab)^2
= (11)^2 + 4(-1)^2
= 121 + 4
= 125