Help with example from AS Pure Maths Book. Watch

ineedthosegrades
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Hi, In the Pure Maths Edexcel Year 1/AS Book there is an example in chapter 7, example 14 about methods of proof, I dont understand why they have done. An explanation would be very helpful, thanks.

https://imgur.com/a/VO39n
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RDKGames
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(Original post by ineedthosegrades)
Hi, In the Pure Maths Edexcel Year 1/AS Book there is an example in chapter 7, example 14 about methods of proof, I dont understand why they have done. An explanation would be very helpful, thanks.

https://imgur.com/a/VO39n
Can you post a clearer image?
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Radioactivedecay
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They simply plugged in values for x and y, one being negative and the other positive, and the result given was -2.5 and because -2.5 is not greater than or equal to 2, the statement doesnt work. This is essentially what proof by counter-example is, you simply find a scenario where the statement doesnt work and you disprove it.
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old_engineer
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(Original post by ineedthosegrades)
Hi, In the Pure Maths Edexcel Year 1/AS Book there is an example in chapter 7, example 14 about methods of proof, I dont understand why they have done. An explanation would be very helpful, thanks.

https://imgur.com/a/VO39n
In part (a), in the jottings section they’ve taken the given expression and shown that it is equivalent to (x - y)^2>=0, which is guaranteed to be positive simply because it is a square. The proof section does pretty much the same in reverse. There is a typo in the text where -2xy wrongly becomes +2xy before being corrected back to negative on the next line.
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ineedthosegrades
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(Original post by old_engineer)
In part (a), in the jottings section they’ve taken the given expression and shown that it is equivalent to (x - y)^2>=0, which is guaranteed to be positive simply because it is a square. The proof section does pretty much the same in reverse. There is a typo in the text where -2xy wrongly becomes +2xy before being corrected back to negative on the next line.
yh but why have they put x^2x+ y^2 - 2xy over xy? where did they get the xy from.
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old_engineer
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(Original post by ineedthosegrades)
yh but why have they put x^2x+ y^2 - 2xy over xy? where did they get the xy from.
They can see that dividing by xy will be a useful step towards rearranging the expression into the required form (and it is part of reversing the stages in the jottings section). Notionally, the 0 on the RHS must also be divided by xy, but they haven't shown that, as 0 / xy = 0 as long as neither x nor y is zero.

You may recall the rule of inequalities that says that if we divide the expression by a negative quantity we must reverse the direction of the inequality. However, we are told at the start that x and y are positive so xy must be positive and the direction of the inequality can stay as it is.
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