Question

if 1-x8 = 65 and 1-x4=64 then what is x

1/2 x root2, root2, 1/root2, 2root2, 3root2

Answer 1

Answer: Let 1- x8 = 65 ------------------(1)
And,            
1 - x4 = 64                 -------------------(2)
Now simplify equation 1 , As:
18 - x8 = 65
⇒(14)2 − (x4)2 = 65
⇒(14 − x4)(14 + x4)     =65                      [We know (a2 − b2) = (a - b ) (a + b)  ]
From equation (2) ​1 - x4 = 64  , substitute that value and get
⇒ 64 (14 + x4) = 65

⇒ (14 + x4) = 6564

⇒x4 =  6564 - 1

⇒x4 = 164

⇒x4 = 12×2×2×2×2×2

⇒x4 = 124 22               
Multiply in power on both side by 14, we get

⇒x  = 122√        (Ans)