Solve It ............

G

gudivaka

Dear All,

Please solve it.First of all this equation was solved by great mathematician Ramanujan.

1.Solve this equation :-

√X + Y = 7
X + √Y = 11

This equation is very interesting equation please try it mathematically.
confused.gif

:thanx:
padmaja
 

Steve Prevette

Deming Disciple
Leader
Super Moderator
Subtract Y from both sides of the first formula

sqrt(x) = 7 - y

Square both sides

x = 49 - 14y + y^2

From the second formula

x = 11 - sqrt(y)

So 49 - 14y + y^2 = 11 - sqrt(y)

38 - 14y + y^2 + sqrt(y) = 0

You can use Excel solver to find the answer (find the eigenvalues). However, be careful since we did square the first formula - be sure to try your answers back in the original formula.
 
R

Roland Cooke

Subtract Y from both sides of the first formula

sqrt(x) = 7 - y

Square both sides

x = 49 - 14y + y^2

From the second formula

x = 11 - sqrt(y)

So 49 - 14y + y^2 = 11 - sqrt(y)

38 - 14y + y^2 + sqrt(y) = 0

Well yeah, that's as far as I got on paper. :D Then my brain melted..... :eek:
 

Steve Prevette

Deming Disciple
Leader
Super Moderator
Well yeah, that's as far as I got on paper. :D Then my brain melted..... :eek:

That formula is as far as you can go algebraically. Now we turn it over to Excel solver to solve by trial and error, or you can graph the funtion in Excel or a graphing calculator, and find out where it crosses zero.
 

Pancho

wikineer
Super Moderator
If you restate A = √X and B = √Y, you can see that these are two intersecting parabolas. One has its axis on the A axis and an intercept at A =7, and the other in the B axis, with the intercept at B = 11.

The parabolas intersect 4 times, once in each quadrant (of the A-B plane).

In the second quadrant, A = -2.8050, B = 3.1313, X = A^2 = 7.8683, Y = B^2 = 9.8050.

Third and fourth quadrant solutions are assigned for homewoik. Show your work! :D
 
A

achorste

:mad:This is really annoying me now - surely theres an analytical method of determining the solution?

Goes of googling.............:read:
 

Steve Prevette

Deming Disciple
Leader
Super Moderator
If you restate A = √X and B = √Y, you can see that these are two intersecting parabolas. One has its axis on the A axis and an intercept at A =7, and the other in the B axis, with the intercept at B = 11.

The parabolas intersect 4 times, once in each quadrant (of the A-B plane).

In the second quadrant, A = -2.8050, B = 3.1313, X = A^2 = 7.8683, Y = B^2 = 9.8050.

Third and fourth quadrant solutions are assigned for homewoik. Show your work! :D

The problem is that the 7.86 and 9.805 DON'T give the proper answers in the original formulae. I got sucked off in that direction also, but then deleted the message. The problem is (-X)^2 and (X)^2 are the same thing, so you have added in three likely false answers by squaring both formulae.
 
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