Question

if x^2+1/x^2=7 find x-1/x. x+1/x...
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Answer 1

Answer:√5,3

Step-by-step explanation:

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

Similarly, (x-1/x)^2=x^2+1/x^2-2

(x+1/x)^2=7+2=9

(x+1/x)=3

(x-1/x)^2=7-2=5

(x-1/x)=√5

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Answer 2

1..(x^2 + 1/x^2) = 7

add and subtract 2 in LHS

x^2 + 1/x^2 + 2 - 2 = 7

(x + 1/x)^2 - 2 = 7

(x + 1/x)^2 = 7 + 2

(x + 1/x)^2 = 9

(x + 1/x) = ✓9

(x + 1/x) = 3

same for .... (x - 1/x)

(x^2 + 1/x^2) = 7

add and subtract 2 in LHS

x^2 + 1/x^2 + 2 - 2 = 7

(x - 1/x)^2 + 2 = 7

(x - 1/x)^2 = 7 - 2

(x - 1/x)^2 = 5

(x - 1/x) = ✓5