Question

If x² – 16x – 59 = 0, then what is the value of (x – 6)² + [1/(x – 6)²]?​

Answer 1

•As

x² – 16x – 59 = 0

or,x² –( 2×8×x)+64 –64 – 59 = 0,

or,x² – 16x +64 = 123

or,( x-8)² = 123

or, x= root 123 + 8 or -(root123) + 8

(x-6) = root123 + 8 - 6 = 13.09

and (x-6) = -(root123) + 8 = -9.03

so, the value of (x – 6)² + [1/(x – 6)²] is

= (root 123 +8 – 6)² + [1/(root 123 +8 – 6)²]

= (13.09)² + [1/(13.09)²]

= 172.38(when x= 13.09)

and when x= -9.03

the value of (x – 6)² + [1/(x – 6)²] is

= (-root 123 +8 – 6)² + [1/(-root 123 +8 – 6)²]

= 82.6