If x+1/x= √5 find these x^2+1/x^2

Question

this is a question from the chapter algebraic expressions

Answer 1

x+(1/x)=√5

x^2+(1/x^2)=???

x+(1/x)=√5

square both sides

x^2+(2)(x)(1/x)+(1/x^2)=5

x^2+(2)(1)+(1/x^2)=5        (x and 1/x are reciprocals so their product is equal to 1)

x^2+2+(1/x^2)=5

x^2+(1/x^2)=5-2

x^2+(1/x^2)=3