If m^2+m^-2=23;then what is the value of m^3+m^-3?
Answers
Answer: 110
Step-by-step explanation:
Given- m^2 + m^-2 = 23
Step 1 → m^2 + 1/m^2 = 23
Both side +2
( m^2 + 1/m^2) + 2 = 23+2
(m^2 + 1/m^2) + 2 = 25
Formula - (x + 1/x)^2 = (x^2 + 1/x^2 + 2*x*1/x)
(x^2 + 1/x^2 + 2) = (x + 1/x)^2
step 2 → So (m^2 + 1/m^2) + 2 = 25
(m + 1/m)^2 = 25
(m + 1/m) = √25
(m + 1/m) = 5-----------(1)
Formula - (m + 1/m)^3 = m^3 + 1/m^3 + 3* m^3*1/m^3 (m+1/m)
(m + 1/m)^3 = m^3 + 1/m^3 + 3* (m+1/m)
m^3 + 1/m^3 = (m + 1/m)^3 - 3* (m+1/m)
→ put the value from eq. (1)
m^3 + 1/m^3 = ( 5)^3 - 3*5
m^3 + 1/m^3 = 125 - 15
m^3 + 1/m^3 = 110