Let t = ⁷√(x-7) , r = ⁷√(x-9) , and ⁷√128 =2 (#) From (#) => x-7 = t⁷ , x-9 = r⁷ => t⁷ - r⁷ = 2 (*) The given equation is written t = r + 2 (**) From (*) and (**) => (r +2)⁷ - r⁷ = 2 => 14( r+1)² (r⁴ +4 r³ +11 r² + 14 r +9) = 0 => r = - 1. From (#) => ⁷√(x-9) = -1=> x-9 = - 1 => x = 8 ( the solution satisfy the given equation).
Let t = ⁷√(x-7) , r = ⁷√(x-9) ,
and ⁷√128 =2 (#)
From (#) => x-7 = t⁷ , x-9 = r⁷ =>
t⁷ - r⁷ = 2 (*)
The given equation is written
t = r + 2 (**)
From (*) and (**) => (r +2)⁷ - r⁷ = 2 =>
14( r+1)² (r⁴ +4 r³ +11 r² + 14 r +9) = 0 =>
r = - 1.
From (#) => ⁷√(x-9) = -1=> x-9 = - 1 =>
x = 8 ( the solution satisfy the given equation).
X= 8 only real soln
x = 8 , the only real solution.
t-1=0
t=1
uv=1
v=1/u
u+v=2
u+(1/u)=2
u²-2u+1=0
∆: b²-4ac
: (-2)²-4•1•1
: 4-4
: 0
u= (-b±0)/2a
u= (2±0)/2
u=1
u=⁷√(x-7)
⁷√(x-7)=1
x-7=1
x=8 #