Okay, I am doing this maths homework in Core 1 Proofing unit
The question asks me to decide if this conjecture is telling the truth.
IF it's true i have to prove it by suitable method and name the method
IF it isn't true, i have to come up with a counterexample
and the questions are as follows
1.The sum of any three consecutive integers is divisible by 6
2. An easy way to remember 7times 8 is that 56=7*8 and the number 5,6,7 and 8are consecutive. There is exactly one other multification of two singledigit numbers with the same pattern
3. x^2>x => x.1
4. ABCD is a parallelogram. Sides AB and DC are parallel; sides AD and BC are parallel. AC=BD
5. A triangle with sides (x^2+1), (x^21), 2x is right angled.
6. The circle with equation x^2+y^2=36 passes through exactly four points for which both the x and y coordinates are integers.
7. The value of (n^2+n+41) is a prime number for all positive integer values of n.
8.A number is divisible by 9 if the sum of its digits is divisible by 9.
9. n is prime, then n^2+n+1 is also a prime
thank you!

ucjs2
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 11112015 01:45

BuryMathsTutor
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 11112015 07:44
(Original post by ucjs2)
Okay, I am doing this maths homework in Core 1 Proofing unit
The question asks me to decide if this conjecture is telling the truth.
IF it's true i have to prove it by suitable method and name the method
IF it isn't true, i have to come up with a counterexample
and the questions are as follows
1.The sum of any three consecutive integers is divisible by 6
2. An easy way to remember 7times 8 is that 56=7*8 and the number 5,6,7 and 8are consecutive. There is exactly one other multification of two singledigit numbers with the same pattern
3. x^2>x => x.1
4. ABCD is a parallelogram. Sides AB and DC are parallel; sides AD and BC are parallel. AC=BD
5. A triangle with sides (x^2+1), (x^21), 2x is right angled.
6. The circle with equation x^2+y^2=36 passes through exactly four points for which both the x and y coordinates are integers.
7. The value of (n^2+n+41) is a prime number for all positive integer values of n.
8.A number is divisible by 9 if the sum of its digits is divisible by 9.
9. n is prime, then n^2+n+1 is also a prime
thank you!
2) Write it in a general form. . Solve this.Last edited by BuryMathsTutor; 11112015 at 07:46. 
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 11112015 09:18
(Original post by ucjs2)
Okay, I am doing this maths homework in Core 1 Proofing unit
The question asks me to decide if this conjecture is telling the truth.
IF it's true i have to prove it by suitable method and name the method
IF it isn't true, i have to come up with a counterexample
and the questions are as follows
1.The sum of any three consecutive integers is divisible by 6
2. An easy way to remember 7times 8 is that 56=7*8 and the number 5,6,7 and 8are consecutive. There is exactly one other multification of two singledigit numbers with the same pattern
3. x^2>x => x.1
4. ABCD is a parallelogram. Sides AB and DC are parallel; sides AD and BC are parallel. AC=BD
5. A triangle with sides (x^2+1), (x^21), 2x is right angled.
6. The circle with equation x^2+y^2=36 passes through exactly four points for which both the x and y coordinates are integers.
7. The value of (n^2+n+41) is a prime number for all positive integer values of n.
8.A number is divisible by 9 if the sum of its digits is divisible by 9.
9. n is prime, then n^2+n+1 is also a prime
thank you!Last edited by Zacken; 11112015 at 11:56. 
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 11112015 09:23
(Original post by ucjs2)
6. The circle with equation x^2+y^2=36 passes through exactly four points for which both the x and y coordinates are integers.
7. The value of (n^2+n+41) is a prime number for all positive integer values of n.
7. Use a nice large counterexample. 
Andy98
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 11112015 09:29
(Original post by ucjs2)
Okay, I am doing this maths homework in Core 1 Proofing unit
The question asks me to decide if this conjecture is telling the truth.
IF it's true i have to prove it by suitable method and name the method
IF it isn't true, i have to come up with a counterexample
and the questions are as follows
1.The sum of any three consecutive integers is divisible by 6
2. An easy way to remember 7times 8 is that 56=7*8 and the number 5,6,7 and 8are consecutive. There is exactly one other multification of two singledigit numbers with the same pattern
3. x^2>x => x.1
4. ABCD is a parallelogram. Sides AB and DC are parallel; sides AD and BC are parallel. AC=BD
5. A triangle with sides (x^2+1), (x^21), 2x is right angled.
6. The circle with equation x^2+y^2=36 passes through exactly four points for which both the x and y coordinates are integers.
7. The value of (n^2+n+41) is a prime number for all positive integer values of n.
8.A number is divisible by 9 if the sum of its digits is divisible by 9.
9. n is prime, then n^2+n+1 is also a prime
thank you! 
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 11112015 09:33
(Original post by Andy98)
5: Find x, if it solves for a real value it is right angled; otherwise it's not. 
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 11112015 09:37
(Original post by Zacken)
You don't really need to find do you? You can just look at the discriminant? 
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 11112015 09:38
(Original post by Andy98)
Well you can do, but I just can't find it in me to use an equation but not solve it if it is solvable. 
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 11112015 09:43
(Original post by Zacken)
Fair enough. 
BuryMathsTutor
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 11112015 11:04
(Original post by Andy98)
5: Find x, if it solves for a real value it is right angled; otherwise it's not. 
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 11112015 11:53

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 11112015 11:55
(Original post by atsruser)
Apropos your questions on another thread, please note that your final implication here is false. (Think about the graph of ) 
DFranklin
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 11112015 13:35
(Original post by Andy98)
5: Find x, if it solves for a real value it is right angled; otherwise it's not.
(It would be a valid answer if the question was "There exists x such that the triangle with sides x^2+1, x^21 and 2x is right angled", but as it stands the question wants you to show it for all x). 
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 11112015 15:00
(Original post by DFranklin)
This is not a valid answer IMHO.
(It would be a valid answer if the question was "There exists x such that the triangle with sides x^2+1, x^21 and 2x is right angled", but as it stands the question wants you to show it for all x). 
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 11112015 15:01
(Original post by Zacken)
Off the top of my head, would you use the cosine rule and solve for and show that ? 
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 11112015 15:04
i) is false... if you add 2, 1, 0 you get 3
no thank you 
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 11112015 15:09
(Original post by DFranklin)
Just use Pythagoras. It's a 1liner. 
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 11112015 15:13
(Original post by Zacken)
Isn't that what Andy did? Or were your remarks directed towards his "find" when he should have said "prove that this identity holds"? 
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 11112015 15:20
(Original post by DFranklin)
At the point where he said "if it solves for a real value" (emphasis mine) it was clear he wasn't looking to show it held for general values of x. 
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 11112015 16:22
(Original post by DFranklin)
At the point where he said "if it solves for a real value" (emphasis mine) it was clear he wasn't looking to show it held for general values of x.
I was just meaning if you can solve it without having to play around with
Posted from TSR MobileLast edited by Andy98; 11112015 at 16:23.
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