Sy123
This too shall pass
- Joined
- Nov 6, 2011
- Messages
- 3,730
- Gender
- Male
- HSC
- 2013
We are doing mathematics here, although you want to take a non-rote approach to maths, asking yourself these kinds of questions will lead to you roting everything (if thats what you want thats your choice). In mathematics sometimes you need to do something different, with enough practise and exposure to different types of questions you gain experience in these sort of matters. We cant always ask ourselves 'I have to ALWAYS do X, then I ALWAYS have to do Y'Do you always have to do both sum and products? and How come you have two unknowns in the equation? aren't you suppose to have one?
It doesnt work like that. We have to observe the question and see where it takes us. We test both because having only ONE equation doesnt do us any good. So hence we go for a second equation. If we found that the first equation was ENOUGH, then we stop and solve.
You can take whatever path you like as long as you find a way to eliminate alpha. Square rooting it is pretty much leading you to the same thing since in the end you must square both sides to eliminate the square root, try your own algebraic approach you end up doing the same thing.Why don't you find alpha by square rooting the RHS? instead of keeping it as alpha squared?
Note how one equation has alpha and one has alpha squared (because we multiplied alpha by alpha). So to eliminate alpha we must make it such that the LHS of BOTH equations are the same, then we can eliminate LHS and solve for the RHS (this is in essence what solving simultaneously by elimination is) Feel free to take whatever algebraic approach you are comfortable with as long as it leads you to the answer (and its short)Why alpha squared and not alpha?
I didnt want to write the whole fraction for the 0.5 one since its tedious:What lol. How is the (k+1)2 the numerator?
I just skipped the algebraic mishap, disregard it though, I divided both sides by 1/4, then by (k+1) (which is incorrect). Look at my above postHow does the whole thing equal to 0... One line it's a fraction with squares and the next line it's 0...