2x+1...square rooted?
If x + 1 = 2 0 1 4 2 + 2 0 1 5 2 , what is 2 x + 1 ?
The answer is 4029.
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2 solutions
Oh... I think you might have a better solution than I do... I didn't factor...
Dear Victor
Please state your source for this question and all questions you post
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Sure, 'D D'
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You know who I am?
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Of course. Do you mind me stating your name?
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@Victor Loh – You still did not state the source
I know you hate this question XD
The sum of 2014 and 2015... Very strange... I worked it out with a calculator but it appears that the answer is 2014 plus 2015. Okay, I'm going to prove this as I go along. First we substitute x into the equation that we are trying to solve. The square root of 2 times 2014 squared plus 2 times 2015 squared minus one. Taking the square root, we find that we can break it into two parts: the square root of 2014 squared and the square root of 2015 squared.... Or just 2014 plus 2015, 4029.
TO GENERALIZE THE PROBLEM
Consider 2 numbers a , b where b = a + 1
x + 1 = a 2 + b 2
substitute b = a + 1
x + 1 = a 2 + ( a + 1 ) 2
x + 1 = a 2 + a 2 + 1 + 2 a
x = 2 a 2 + 2 a
Now substitute the value of x in given equation
2 x + 1
2 ( 2 a 2 + 2 a ) + 1
4 a 2 + 4 a + 1
If you observe, the given equation can be factorised
( 2 a + 1 ) 2
2 a + 1
a + a + 1
ie a + b
So the value of 2 x + 1 = a + b
Ans 4 0 2 9
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This is a lot easier than mine, almost no calculations.
I'm just kinda confused that how you broke it into two parts, could you explain it to me?
First we move the +1 to the right side and we get x=2014^2+2015^2-1 Factoring 2015^2-1 we get (2015+1)(2015-1) which equals 2016x2014 For x=2014^2+2014x2016 we take 2014 out. Thus we get x=2014(2014+2016)=2014x4030 2x=2x2014x4030=4028x4030=(4029-1)(4029+1)=4029^2-1 2x+1=4029^2 Therefore the square root of 2x+1 equals to 4029
I'll never use iPad to type those numbers and signs again:-(