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:

Value of m + 1/m is 6 and m³ + 1/m³ is 198.

Step-by-step explanation:

m² + 1/m² = 34

Adding 2 on both sides

m² + 1/m² + 2 = 34 + 2

It can be written as

m² + ( 1/m )² + 2( m )( 1/m ) = 36

( m + 1/m )² = 36

Since a² + b² + 2ab = ( a + b)²

m + 1/m = √36 = 6

Cubing on both sides

( m + 1/m )³ = 6³

m³ + ( 1/m )³ + 3( m )( 1/m )( m + 1/m ) = 216

Since ( a + b)³ = a³ + b³ + 3ab( a + b)

m³ + 1/m³ + 3( 6 ) = 216

m³ + 1/m³ + 18 = 216

m³ + 1/m³ = 216 - 18 = 198

Therefore the value of m + 1/m is 6 and m³ + 1/m³ is 198.