Question

If x+1\x=root5, find the value of x^2+1\x^2 and x^4+1\x^4

Answer 1

Step-by-step explanation:

x+1/x = √5

(x+1/x)^2=(√5)^2

x^2+2 × x ×1/x + (1/x)^2 = 5

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

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

x^2+1/x^2=3

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

x^4+2× x^2 ×1/x^2 +1/x^4=9

x^4+2+1/x^4=9

x^4+1/x^4=9-2

x^4+1/x^4=7

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