Algebra-29

If (x²+1)/x = 5, then find the value of (x¹²+1)/x⁶?

(1)120098      (2) 5    (3) 12100       (4) 5⁶   (5) none of these

Solution follows here:

Solution:

This is a bit changed in shape from the traditional one,

“If x + 1/x = 5 then find x⁶ + 1/x⁶ “

As we need to find 6th power, first we proceed for cube

x + 1/x = 5 => (x + 1/x)³ = 5³
Formula to be used here : (a+b)³ = a³+b³+3ab(a+b)

=> x³ + 1/x³ + 3x(1/x)(x+1/x) = 125

=> x³ + 1/x³ + 3 (5) = 125

=> x³ + 1/x³ = 110

Now squaring on both sides,
(x³ + 1/x³)²  = 110²

Formula to be used here : (a+b)² = a²+b²+2ab
=> x⁶ + 1/x⁶ + 2x³(1/x³) = 12100

=> x⁶ + 1/x⁶ + 2 = 12100

=> x⁶ + 1/x⁶ = 12098
Be careful at the answer options, 120098 is given to trap.

Answer (5)