Question

How to do this :
sqrt(A) + sqrt(B) + 2sqrt(C-3) + sqrt(D) + sqrt(E) =
A+B+C+D+E+1. Determine the value of A*B*C*D*E

Answer 1

Are there answer options?

Answer 2

What? Don't you need 5 equations to solve 5 variables?

Answer 3

no options, and no information what's kind number for A,B,C,D, and E. but i guess they are integer numbers.

Answer 4

@NewOne luckily 5 variables aren't being solved for...

Answer 5

You can combine them all to form one single root.

Answer 6

@tanjung they can't be integers, sorry.

Answer 7

Oh wait this is addition, sorry. No you can't.

Answer 8

@tanjung are you sure it's addition?

Answer 9

yes.. i think there is the special way to solve this, but i dont know.. it is an olympiad problem :)

Answer 10

I think you can just set them each equal to each other and solve for each variable. I didn't read the full question. I thought it was = 0

Answer 11

@abb0t if it were equal to 0 and you were interested in only real solutions, then A*B*C*D*E = 0 as well :-)

Answer 12

Yeah, but they are = A + B + C ... 1

Answer 13

any idea guys ?
@AccessDenied , @experimentX , @Callisto ,@ganeshie8 @ghazi

Answer 14

just put up 111 for 4 for c

Answer 15

Since we have no constraints, make a, b, d, and e equal 0. Then, we solve 2sqrt(c-3) = c + 1

Answer 16

This gives an imaginary solution. If you need the solution to be a real number, then you'll have to rethinking which values you choose for a, b, ...

Answer 17

i think the last term should be -1, not +1... so that the equation can be a perfect square and to get a real solution!

Answer 18

i assumed the last term is -1, so
A+B+C+D+E-1=sqrt(A)+sqrt(B)+2sqrt(C-3)+sqrt(D)+sqrt(E)

A-sqrt(A)+B-sqrt(B)+C-sqrt(C-3)+D-sqrt(D)+E-sqrt(E)-1=0

(sqrt(A)-1/2)^2 - 1/4 + (sqrt(B)-1/2)^2 - 1/4 + (sqrt(C-3)-1)^2 + 2 + (sqrt(D)-1/2)^2 - 1/4 + (sqrt(E)-1/2)^2 - 1/4 - 1 = 0

(sqrt(A)-1/2)^2 + (sqrt(B)-1/2)^2 + (sqrt(C-3)-1)^2 + (sqrt(D)-1/2)^2 + (sqrt(E)-1/2)^2 = 0

it must satisfies if all perfect squares in LHS will be zero.
therefore,
sqrt(A) = 1/2 -----> A=1/4
sqrt(B) = 1/2 -----> B=1/4
sqrt(C-3)=1 ------->C=4
sqrt(D) = 1/2 -----> D=1/4
sqrt(D) = 1/2 -----> E=1/4
so, the value of A*B*C*D*E = ....

Answer 19

Good catch, RadEn.

I don't see how it's possible to get a real solution otherwise. I was just trying to solve 4*sqrt(x) = 3 + 4x... If instead of +1 we have -1, then it's 4sqrt(x) = 2+4x, which does have a real solution. (a=b=d=e=1/4)

Answer 20

opsss.. the last shoulde be
sqrt(E) = 1/2 -----> E=1/4, :)

Answer 21

sqrt(A) <A , sqrt(B) <B, 2sqrt(C-3) <C , sqrt(D)<D , sqrt(E)<E
so,
sqrt(A) + sqrt(B) + 2sqrt(C-3) + sqrt(D) + sqrt(E)<A + B + C + D + E

Answer 22

so, I guess it must be -1 as @RadEn said

Answer 23

Btw, saurav, sqrt(A) is greater than A if A < 1

Answer 24

@sauravshakya your premises are faulty if they're in (0,1)

Answer 25

But all variables cannot be 0 or 1

Answer 26

So, if only one variale is non zero and it is not 1 then it must be
sqrt(A) + sqrt(B) + 2sqrt(C-3) + sqrt(D) + sqrt(E)<A + B + C + D + E

Answer 27

@sauravshakya that's not what (0,1) means...
http://en.wikipedia.org/wiki/Interval_(mathematics)#Notations_for_intervals

Answer 28

saur, to make this problem have a real solution, start off by making c = 3. So now we have sqrt(A) + ... + sqrt(E) = A + B + D + E + 4. Assume A=B=D=E, then we have 4*sqrt(x) = 4x + 4. This has no real solution, but if we take Rad's advice, and make the +1 a -1, then it does.

Answer 29

I was also trying to say the same thing

Answer 30

to have a real solution it must be -1

Answer 31

*nods*