Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    17
    ReputationRep:
    Expand and simplify:
    2x^1/2(x^1/2-x^-1/2)
    I am not very sure how to solve this.
    Thank you in advance fellow TSRians.
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by Wolfram Alpha)
    Expand and simplify:
    2x^1/2(x^1/2-x^-1/2)
    I am not very sure how to solve this.
    Thank you in advance fellow TSRians.
    Expand as you normally would.

    And use the fact that \displaystyle x^a \times x^b \equiv x^{a+b}.

    Post your working if you get stuck.
    Offline

    0
    ReputationRep:
    add the outer power by the inner power of each while putting a 2 in front , 2x1X^1/2+1/2 - 2x1X^1/2+(-1/2) and simplify it to 2X-2
    • Thread Starter
    Offline

    17
    ReputationRep:
    (Original post by notnek)
    Expand as you normally would.

    And use the fact that \displaystyle x^a \times x^b \equiv x^{a+b}.

    Post your working if you get stuck.
    I multiplied 2x^1/2 by x^1/2 which gives 2x. Then 2x^1/2 multiplier by x^-1/2 which gives 2x^0. So would the answer just be 2x + 1?
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by Wolfram Alpha)
    I multiplied 2x^1/2 by x^1/2 which gives 2x. Then 2x^1/2 multiplier by x^-1/2 which gives 2x^0. So would the answer just be 2x + 1?
    2x is correct.

    But it should be -2x^0 instead of 2x^0. Can you see why?

    And 2x^0 = 2 \times x^0 = ...
    • Thread Starter
    Offline

    17
    ReputationRep:
    (Original post by notnek)
    2x is correct.

    But it should be -2x^0 instead of 2x^0. Can you see why?

    And 2x^0 = 2 \times x^0 = ...
    Ah, I have just noticed the negative sign. So -2x^0 gives -2 rather than zero. Thus the final answer is 2x-2. I thank you for your time. It is much appreciated.
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by Wolfram Alpha)
    Ah, I have just noticed the negative sign. So -2x^0 gives -2 rather than zero. Thus the final answer is 2x-2. I thank you for your time. It is much appreciated.
    Correct
    • Thread Starter
    Offline

    17
    ReputationRep:
    (Original post by regan1234567)
    add the outer power by the inner power of each while putting a 2 in front , 2x1X^1/2+1/2 - 2x1X^1/2+(-1/2) and simplify it to 2X-2
    Regan, thank you for your answer.
    • Thread Starter
    Offline

    17
    ReputationRep:
    (Original post by notnek)
    Correct
    I have one more question friend. (3x^1/2 - 2x^-1/2)(2x^1/2 - 3x^-1/2) equals 6x - 13 + 1/6x. Am I correct?
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by Wolfram Alpha)
    I have one more question friend. (3x^1/2 - 2x^-1/2)(2x^1/2 - 3x^-1/2) equals 6x - 13 + 1/6x. Am I correct?
    Nearly but 1/6x is incorrect.

    \displaystyle -2x^{-\frac{1}{2}} \times -3x^{-\frac{1}{2}} = 6x^{\left(-\frac{1}{2} - \frac{1}{2}\right)} = 6x^{-1} = 6 \times x^{-1} = ...
    • Thread Starter
    Offline

    17
    ReputationRep:
    (Original post by notnek)
    Nearly but 1/6x is incorrect.

    \displaystyle -2x^{-\frac{1}{2}} \times -3x^{-\frac{1}{2}} = 6x^{\left(-\frac{1}{2} - \frac{1}{2}\right)} = 6x^{-1} = 6 \times x^{-1} = ...
    I thought 6x^-1 was 1/6x. I am clearly wrong. Could you please enlighten me?
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by Wolfram Alpha)
    I thought 6x^-1 was 1/6x. I am clearly wrong. Could you please enlighten me?
    Both are wrong but It's not clear if 1/6x means \frac{1}{6}x or \frac{1}{6x}.


    Explanation :

    You know that \displaystyle x^{-1} = \frac{1}{x}

    So \displaystyle 6x^{-1} = 6 \times x^{-1} = 6 \times \frac{1}{x} = \frac{6}{1} \times \frac{1}{x} = \frac{6}{x}


    It will be useful for you to become familiar with this rule : \displaystyle ax^{-n} = \frac{a}{x^n}

    E.g. \displaystyle 6x^{-1} = \frac{6}{x} or \displaystyle 4x^{-3} = \frac{4}{x^3}.
    • Thread Starter
    Offline

    17
    ReputationRep:
    (Original post by notnek)
    Both are wrong but It's not clear if 1/6x means \frac{1}{6}x or \frac{1}{6x}.


    Explanation :

    You know that \displaystyle x^{-1} = \frac{1}{x}

    So \displaystyle 6x^{-1} = 6 \times x^{-1} = 6 \times \frac{1}{x} = \frac{6}{1} \times \frac{1}{x} = \frac{6}{x}


    It will be useful for you to become familiar with this rule : \displaystyle ax^{-n} = \frac{a}{x^n}

    E.g. \displaystyle 6x^{-1} = \frac{6}{x} or \displaystyle 4x^{-3} = \frac{4}{x^3}.
    Ah, I see! I was aware of that rule but I suppose I got confused when applying it. Mhmm, thanks for your help again.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    What's your favourite Christmas sweets?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.