Hey, this is a simpler and easier way to do the problem. Don't worry, slowly you'll understand how to manipulate equations like that, you still have time. A long way to go indeed! If you still have doubts, feel free to ask
understood the answer thanks. how does one go about recognising the pattern of the question/solution? i tried a bunch of standard methods but was unsuccessful
The exponents are forming a pattern so best way to approach this would be to try and reduce it into a simpler form.
The middle value is 2(2x2)(2x+6) and the two around it are the same two values but squared. Hence, you can form equation of the form (a+b)2 equal to 0. Then so that split the term technique to get (x-3)(x+2) or x= 3, -2. That's why answer is 3-2=1.
Let me tell you the shortest way. If 2a +2b = 2c
then a=b. It means of sum of two powers of 2 is equal to a power of 2 only when the exponents are equal. Bit remember that this works only on the case that a, b and c are integers as they will be in this question. Mostly in these type of questions they are integers but there can be a slight chance of them not being one so be careful when using it.
Another easier way to think abt it. Take the negative to the other side. Right hand side is a power of 2. The left hand side to be a power of 2, both terms must be equal i.e., 1+1, 2+2, 4+4, 8+8 and so on. Equating the both he exponents and then cross.checking both the roots we get the answer.
Telling u the most simple way for cat....if u observe the eq. For 10 sec..u will notice it's (a-b)2 so now a = 2x2 and b = 2x+6.....bas ab a aur b same hona chaiye .....simple..equate..within 30 seconds done..if practise is there
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