Question

What is the difference in the sum of the squares & the difference of squares of 'n' & 'a' when \[\LARGE{\frac{\sqrt{a^{n-2}.3^{a+2}}}{6^n.\left( n \over 2 \right)-\left( 1-{n \over 2} \right)}=\frac{1}{4\sqrt{2^n}}}\] & sum of 'a' & 'n' is 12:

Answer 1

@mukushla @ParthKohli @TuringTest @amistre64 plz help:)

Answer 2

that looks like a whole lotta algebra

Answer 3

looks like you should prolly get rid of the radicals, turn them into exponents; cross multiply, and work it from there

Answer 4

i need full solution plz:)

Answer 5

then you really should work at it ....

Answer 6

at the moment, its a bit hectic, but it can be made to look better by using basic algebraic principles

Answer 7

@mathslover @experimentX @apoorvk can u give me full solution to this ques:)

Answer 8

Why not i can give but only if i understand ... I am going to do that now

wait

Answer 9

k!

Answer 10

is the answer \(\Huge{2a^2}\)

Answer 11

@jiteshmeghwal9 ?

Answer 12

what is the question? I mean , what are we supposed to find

Answer 13

What is the difference in the sum of the squares & the difference of squares of 'n' & 'a' @vamgadu

Answer 14

that means we have to find 2a^2

Answer 15

yes hence i asked him that is the answer : 2a^2 :D

Answer 16

I think we should find a more numeric answer

Answer 17

:P

Answer 18

no ! the answer is 50 :/

Answer 19

ok, I'll proceed from here in this manner.
the RHS is does not have a power of 3, where as the LHS has an exponent of 3.
so I would say the exponent of 3 in the LHS should become 0. I am working under the assumption that a is not a multiple of 3. If I get an absurd proceeding this way I'll come back and say"Dude, my assumption was wrong. so a is a multiple of 3"
Now using this assumption, power of 3 in th LHS should become 0, which means a+2-n=0
we already have a+n=12.
that gives n=7 and a=5 which is consistent with the assumption that a is not a multiple of 3.
so the answer become 2a^2=50

Answer 20

If you still are ambiguous about the solution or you need to present it some where,
I would suggest assuming a is a multiple of 3 as the first case and prove it leads to an absurd

Answer 21

can't we find the answer without assumption

Answer 22

i am not assuming any thing.
I basically am dividing the solution into 2 cases.
case 1: if a is a multiple of 3.
proceed in this manner and this should leads to an absurd.
case 2: as case 1 is an absurd, a is not a multiple of 3 and proceed in the manner I posted. I think this is the easiest way.

Answer 23

sorry ! but i mn't getting it can u plz tell me through an easy way:)

Answer 24

a is equal to 5 i think
hence 2a^2=2*25=50

Answer 25

ya ! it may be

Answer 26

plz wait. I'll find out another way.:-)

Answer 27

k!

Answer 28

@ParthKohli :)

Answer 29

k! i have closed the ques.

Answer 30

Why @jiteshmeghwal9 ?

Answer 31

Is this of NTSE ?

Answer 32

yes! @mathslover

Answer 33

TMH /?

Answer 34

dude I think there is a mistake with this question. I wrote a code in MATLAB and found the solutions are a=6.26 and n=5.74 and they are consistent with the given equation.so, check the question once and confirm. I'll retry.@jiteshmeghwal9