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Question

If X+ 1/X=  √5 (square root of 5)

find the value of X^2 (x squared) + 1/X^2 

 

 

Answer 1

x²+1/(x²)=3.

 

Take first equation, mulitply everything by x and set equal to zero: x²-sqrt(5)*x+1=0

Solve quadratic: x = [sqrt(5)±1]/2

x²=[3±sqrt(5)]/2

x²+1/x²=3

Answer 2

Starting with the first equation:

 

x + 1/x = sqrt (5)

 

Squaring both sides of the equation gives:

 

(x + 1/x)^2 = 5

 

Multiplying out the left side of the equation gives:

 

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

 

Continuing to simplifY:

 

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

 

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

 

 

 

 

 

Answer 3

X + 1/X = √5

 

If we square this we have

X² + 2(X/X) + 1/x² = 5

X² + 2 + 1/x² = 5

X² + 1/x² = 5 - 2 = 3