Question

If m2+1/m2=34,find the value of m3+1/m3 using only the positive value of m+1/m.Pls answer!!!!?!?

Answer 1

Answer:

198

Step-by-step explanation:

Given:

$\\\tt m^2 + \dfrac{1}{m^2} = 34$

Make a perfect square on RHS add 2 both sides:

$\\\tt m^2 + \dfrac{1}{m^2} + 2(m)(\dfrac{1}{m}) = 36$

$\\\tt (m + \dfrac{1}{m} )^2 = 36$

Find value for $\\\tt m + \dfrac{1}{m}$ which here turns out to be 6.

Cubing both sides:

$\\\tt (m + \dfrac{1}{m} )^3 = 216 \\\tt m^3 +\dfrac{1}{m^3} + 3(m)(\dfrac{1}{m})(m + \dfrac{1}{m}) = 216 \\\tt m^3 +\dfrac{1}{m^3}+ 3(6) = 216 \\\tt m^3 +\dfrac{1}{m^3} = 198$