Question

6 find the value of (x+ 2) 2 ( x -+ ) 2.(x+1/x)^2-(x-1/x)^2
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Answer 1

Answer:

If x+(1/x)=2, then what is the value of x-(1/x) =?

If x+(1/x)=2, then what is the value of x-(1/x) =?Switch to a safe & enriching sleep experience.

If x+(1/x)=2, then what is the value of x-(1/x) =?Switch to a safe & enriching sleep experience.We may construct two cases, depending on whether x>0, or x<0 ( Obviously x≠0 )

If x+(1/x)=2, then what is the value of x-(1/x) =?Switch to a safe & enriching sleep experience.We may construct two cases, depending on whether x>0, or x<0 ( Obviously x≠0 )Case 1:

If x+(1/x)=2, then what is the value of x-(1/x) =?Switch to a safe & enriching sleep experience.We may construct two cases, depending on whether x>0, or x<0 ( Obviously x≠0 )Case 1:x>0

If x+(1/x)=2, then what is the value of x-(1/x) =?Switch to a safe & enriching sleep experience.We may construct two cases, depending on whether x>0, or x<0 ( Obviously x≠0 )Case 1:x>0 By applying the AM−GM inequality, we get:

If x+(1/x)=2, then what is the value of x-(1/x) =?Switch to a safe & enriching sleep experience.We may construct two cases, depending on whether x>0, or x<0 ( Obviously x≠0 )Case 1:x>0 By applying the AM−GM inequality, we get:x+1/x>=2

If x+(1/x)=2, then what is the value of x-(1/x) =?Switch to a safe & enriching sleep experience.We may construct two cases, depending on whether x>0, or x<0 ( Obviously x≠0 )Case 1:x>0 By applying the AM−GM inequality, we get:x+1/x>=2 With equality holding for the case, x=1/x=1

If x+(1/x)=2, then what is the value of x-(1/x) =?Switch to a safe & enriching sleep experience.We may construct two cases, depending on whether x>0, or x<0 ( Obviously x≠0 )Case 1:x>0 By applying the AM−GM inequality, we get:x+1/x>=2 With equality holding for the case, x=1/x=1 So, x−1/x=0 , for x>0

If x+(1/x)=2, then what is the value of x-(1/x) =?Switch to a safe & enriching sleep experience.We may construct two cases, depending on whether x>0, or x<0 ( Obviously x≠0 )Case 1:x>0 By applying the AM−GM inequality, we get:x+1/x>=2 With equality holding for the case, x=1/x=1 So, x−1/x=0 , for x>0 Case 2:

If x+(1/x)=2, then what is the value of x-(1/x) =?Switch to a safe & enriching sleep experience.We may construct two cases, depending on whether x>0, or x<0 ( Obviously x≠0 )Case 1:x>0 By applying the AM−GM inequality, we get:x+1/x>=2 With equality holding for the case, x=1/x=1 So, x−1/x=0 , for x>0 Case 2:x<0

If x+(1/x)=2, then what is the value of x-(1/x) =?Switch to a safe & enriching sleep experience.We may construct two cases, depending on whether x>0, or x<0 ( Obviously x≠0 )Case 1:x>0 By applying the AM−GM inequality, we get:x+1/x>=2 With equality holding for the case, x=1/x=1 So, x−1/x=0 , for x>0 Case 2:x<0 If x<0 , then so is 1/x .

If x+(1/x)=2, then what is the value of x-(1/x) =?Switch to a safe & enriching sleep experience.We may construct two cases, depending on whether x>0, or x<0 ( Obviously x≠0 )Case 1:x>0 By applying the AM−GM inequality, we get:x+1/x>=2 With equality holding for the case, x=1/x=1 So, x−1/x=0 , for x>0 Case 2:x<0 If x<0 , then so is 1/x .But, if both are less than 0 , then their sum must also be less than 0 , and hence cannot be 2 .

If x+(1/x)=2, then what is the value of x-(1/x) =?Switch to a safe & enriching sleep experience.We may construct two cases, depending on whether x>0, or x<0 ( Obviously x≠0 )Case 1:x>0 By applying the AM−GM inequality, we get:x+1/x>=2 With equality holding for the case, x=1/x=1 So, x−1/x=0 , for x>0 Case 2:x<0 If x<0 , then so is 1/x .But, if both are less than 0 , then their sum must also be less than 0 , and hence cannot be 2 .So, this case is void.

If x+(1/x)=2, then what is the value of x-(1/x) =?Switch to a safe & enriching sleep experience.We may construct two cases, depending on whether x>0, or x<0 ( Obviously x≠0 )Case 1:x>0 By applying the AM−GM inequality, we get:x+1/x>=2 With equality holding for the case, x=1/x=1 So, x−1/x=0 , for x>0 Case 2:x<0 If x<0 , then so is 1/x .But, if both are less than 0 , then their sum must also be less than 0 , and hence cannot be 2 .So, this case is void.Hence, we get:

If x+(1/x)=2, then what is the value of x-(1/x) =?Switch to a safe & enriching sleep experience.We may construct two cases, depending on whether x>0, or x<0 ( Obviously x≠0 )Case 1:x>0 By applying the AM−GM inequality, we get:x+1/x>=2 With equality holding for the case, x=1/x=1 So, x−1/x=0 , for x>0 Case 2:x<0 If x<0 , then so is 1/x .But, if both are less than 0 , then their sum must also be less than 0 , and hence cannot be 2 .So, this case is void.Hence, we get:x−1/x=0 , for all real x satisfying x+1/x=2

Step-by-step explanation:

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