Question

m+1/m = √3 ; value of m^72+m^66+m^54+m^36+m^24+m^6+2​

Answer 1

Step-by-step explanation:

m +1/m = √3…………………(1) , cube the both sides.

or, m^3+3.m.1/m.(m+1/m)+1/m^3= (√3)^3.

or, m^3+3.(√3)+1/m^3 = 3√3.

or, m^3+ 1/m^3= 0

or , m^3 = - 1/m^3.

or, m^6 = -1

Now , m^72+m^66+m^54+m^36+m^24+m^6 +2. = ?

= (m^6)^12+(m^6)^11+(m^6)^9+(m^6)^6+(m^6)^4+(m^6) +2.

Putting m^6= -1.

= (-1)^12+(-1)^11+(-1)^9+(-1)^6+(-1)^4+(-1)+ 2.

= 1 - 1 - 1 + 1+1–1 +2.

= 5 - 3.

= 2. , Answer.✅

✅Hope did this helpful for you❗