If x+1x=4, then x4+1x4=?
Evaluate the given expression
Given equation, x+1x=4
Square on both side,
(x+1x)2=42
By using identity (a+b)2=a2+b2+2ab
⇒x2+(1x)2+2x1x=16⇒x2+(1x)2+2=16⇒x2+(1x)2=16-2⇒x2+(1x)2=14
Again, squaring both sides, ⇒(x2+(1x)2)2=14
⇒x22+1x22+2x21x2=142⇒x22+1x22+2=196⇒x22+1x22=196-2⇒x22+1x22=194
⇒x4+1x4=194
Hence, x4+1x4=194
If x+1x=4, then x4+1x4=
Determine whether the following numbers are in proportion or not:
13,14,16,17