Question

a^4 + b^4 = 47
a.b = 1

a+b= ?

Answer 1

a⁴+b⁴=47 seja a²=K e b²=N
(a²)²+(b²)²=47
(K)²+(N)²=47
(K+N)²-2KN=47
(a²+b²)²-2*a²b²=47. se ab=1 então
(a²+b²)²-2*(ab)²=47
(a²+b²)²-2*(1)²=47
(a²+b²)²=47+2
(a²+b²)=√(49)
a²+b²=7
(a+b)²-2ab=7
(a+b)²-2*1=7
(a+b)²=7+2
(a+b)=√9
a+b=3