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Why does he do this? - GCSE maths

http://www.mrbartonmaths.com/resources/GCSE%20Revision/Past%20Papers/9.%20November%202012/Nov%202012%20-%20Paper%202%20Higher%20-%20Written%20Solutions.pdf

Question 22 ( b )

Why does it become 2/y^2 + 9y/y^2 - 7y/y^2 = 0
-7y^2 + 9y + 2 = 0
??

Thanks, would appreciate if you could tell me why he does this, as I'm stuck.

Also, if you're feeling very helpful, on Q19 why does it go from 8 x 10^8 to 8 x 10^11 in the workings?

Thanks!
Original post by iMacJack
http://www.mrbartonmaths.com/resources/GCSE%20Revision/Past%20Papers/9.%20November%202012/Nov%202012%20-%20Paper%202%20Higher%20-%20Written%20Solutions.pdf

Question 22 ( b )

Why does it become 2/y^2 + 9y/y^2 - 7y/y^2 = 0
-7y^2 + 9y + 2 = 0
??

Thanks, would appreciate if you could tell me why he does this, as I'm stuck.

Also, if you're feeling very helpful, on Q19 why does it go from 8 x 10^8 to 8 x 10^11 in the workings?

Thanks!

22b. He multiplies each term by y2y^2 to get all positive powers of y. The equation is then easy to solve-it's a quadratic.

19. There's a general rule for multiplying indices: abac=ab+ca^ba^c = a^{b+c}. So 108103=101110^{8}10^{3} = 10^{11}.
I think on the first one it is because the three y^2 cancel out, as they are all in the denominator, although I'd ask for confirmation of that. :smile:

Reply 3
Hi, thanks but for no. 19 where did he get the extra 3 powers from I understand the rules of indices but where did he get the extra 8 x 10^3 from
Original post by iMacJack
Hi, thanks but for no. 19 where did he get the extra 3 powers from I understand the rules of indices but where did he get the extra 8 x 10^3 from


The distance between Jupiter and the Sun is given in km. The 10310^3 converts it to metres to compare with the other distance, which is given in metres.

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