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Unsure how to do these questions watch

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    Basically I'm having trouble with these two questions. For the first one I've managed to rationalise the denominator and get (3)^0.5 - (2)^0.5 but I'm unsure how that helps me with the rest of the question and if the answer is simple at all

    For the next question I'm just baffled at how I work with 4 unknowns. Expanding the brackets hasn't helped me much and I can't factorise the x out any further :/

    Any help would be excellent!
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    For the second part of the question, see what you get if you rationalise

    \frac{1}{\sqrt{n}+\sqrt{n+1}}

    then see what happens when you sum them (you should get some cancelling).

    For the second question it is just a quadratic, solve like you would any other quadratic. There is only 1 variable, the a,b,c are all fixed constants (I guess).
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    (Original post by Silverland)
    mathsmathsmaths
    The first one looks right, and about as simple as you can get it. For the sequence, you should simplify each term - but don't do each individually, use your result from the first bit and use the same form. Because each term will be sqrt(a)-sqrt(b), most of the terms will cancel so you'll end up with something like sqrt(100)-sqrt(1). If that is the answer (just a mental estimate) obviously simplify the roots into integers. For the second question, try expanding the brackets, and then complete the square, treating the a, b and c as constants like you would in the quadratic formula.

    Can I ask, is this FP1?
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    Thanks! I've been able to get through the first one and most of the second. For the last bit I'm getting close to the answer but can't remove the awkward "ab" term I get from expanding my brackets. It'd be fine otherwise; by the quadratic forumula or completing the square. hmmy hmm

    (and no, this isn't FP1 but a chemist who is unsure why he likes the physical side of things again)
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    (Original post by Silverland)
    Thanks! I've been able to get through the first one and most of the second. For the last bit I'm getting close to the answer but can't remove the awkward "ab" term I get from expanding my brackets. It'd be fine otherwise; by the quadratic forumula or completing the square. hmmy hmm

    (and no, this isn't FP1 but a chemist who is unsure why he likes the physical side of things again)
    You don't need to get rid of it. Get it in the form \alpha x^2 + \beta x + \gamma = 0 (where \alpha, \beta,\gamma are functions of a, b, c), and use the quadratic formula.
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    http://ipm-mtse-olympiad-state-schol...orization.html
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    (Original post by Silverland)


    Basically I'm having trouble with these two questions. For the first one I've managed to rationalise the denominator and get (3)^0.5 - (2)^0.5 but I'm unsure how that helps me with the rest of the question and if the answer is simple at all

    For the next question I'm just baffled at how I work with 4 unknowns. Expanding the brackets hasn't helped me much and I can't factorise the x out any further :/

    Any help would be excellent!
    most of the hint are enough to solve the equation:
    none the less, if you still need help, check
    http://ipm-mtse-olympiad-state-schol...quation_9.html
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    thanks
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