Question

If y+1/y=3. Then find y^5+1/y^5

Answer 1

Answer:

123

Step-by-step explanation:

$(y+\frac{1}{y} )^2=y^2+\frac{1}{y^2} +2$

$(y+\frac{1}{y} )^3=y^3+\frac{1}{y^3} +3(y+\frac{1}{y} )$

From that, we can get :

$y^2+\frac{1}{y^2}=(y+\frac{1}{y} )^2 -2$,

$y^3+\frac{1}{y^3}=(y+\frac{1}{y} )^3-3(y+\frac{1}{y} )$.

∴$y^2+\frac{1}{y^2}=7$

∴$y^3+\frac{1}{y^3}=18$

$(y^2+\frac{1}{y^2})*(y^3+\frac{1}{y^3})=y^5+\frac{1}{y^5} +y+\frac{1}{y}$

From that, we can get :

$y^5+\frac{1}{y^5} =(y^2+\frac{1}{y^2})*(y^3+\frac{1}{y^3})-(y+\frac{1}{y})$.

∴$y^5+\frac{1}{y^5} =123$