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Unsure how to do these questions



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!
Reply 1
Avatar for james22
james22
16
For the second part of the question, see what you get if you rationalise

1n+n+1\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).
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?
(edited 10 years ago)
Reply 3
Avatar for Silverland
Silverland
OP
3
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)
Reply 4
Avatar for BlueSam3
BlueSam3
17
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 αx2+βx+γ=0\alpha x^2 + \beta x + \gamma = 0 (where α,β,γ\alpha, \beta,\gamma are functions of a,b,ca, b, c), and use the quadratic formula.
(edited 10 years ago)
Reply 5
Avatar for shubhro
shubhro
1
http://ipm-mtse-olympiad-state-scholarship.blogspot.in/2013/10/factorization.html
Reply 6
Avatar for shubhro
shubhro
1
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-scholarship.blogspot.in/2013/10/quadratic-equation_9.html
Reply 7
Avatar for Silverland
Silverland
OP
3
thanks
//

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