Question

solve it fast 16 and 17​

Answer 1

x^2 + 1/x^2 = 23

x^2 + 1/x^2 + 2 (x *1/x) =23+2

(x+1/x)^2 =25

x+1/x =+5 or - 5

a²+b² = 117

ab = 54

as a²+b² = (a+b)²-2ab

therefore

117 = (a+b)²-2*54

117 = (a+b)²-108

117+108 = (a+b)²

225 = (a+b)²

15 = (a+b) ___ (i)

as a²+b² = (a-b)²+2ab

therefore

117 = (a-b)²+2*54

117 = (a-b)²+108

117-108 = (a-b)²

9 = (a-b)²

3 = (a-b) ___ (ii)

from (i) & (ii)

(a+b)/(a-b) = 15/3

(a+b)/(a-b) = 5