Question

sqrt(x) + sqrt(y) =11, find x and y.

Answer 1

can only find x as a function of y, and vice versa given you only have one equation

Answer 2

if you square both sides, you are left with:
x + y = 121

Answer 3

therefore you can re-arrange your equation to either:
x= 121-y
or
y=121 - x

Answer 4

just square and so me how

Answer 5

... what...?

Answer 6

x and y are positive integer numbers ?

Answer 7

@rahulon i think,the information is not enough

Answer 8

Hint : Square both sides.

Answer 9

Sritama, I think it is not necessary to calculate exact values for x and y, they can be in terms of each other.

Answer 10

x and y are real number

Answer 11

if x and y are real numbers, you will need a 2nd equation to find the value of each, as there are 2 unknowns

Answer 12

\((\sqrt{x} + \sqrt{y} )^2 = 11^2\)

\(\implies \sqrt{x}^2 + \sqrt{y}^2 + 2\sqrt{xy} = 121\)
\(\implies x + y + 2\sqrt{xy} =121\)

Answer 13

but what about sqrt(xy)

Answer 14

Sritama and Jack1 are right if you want to get the values for the 2 unknowns , though I can say that :

\(x = 121 - y - 2\sqrt{xy}\)
or
\(y= 121-2\sqrt{xy} - x\)

Answer 15

you're right @mathslover, my bad

Answer 16

@rahulon got it?

Answer 17

emm...i think the questions wants us to get numerical values for x and y if im not wrong..lets work on that

Answer 18

and most likely x and y are integers as RadEn said

Answer 19

I don't think that there is ANY way to calculate the numerical values for x and y as it is an equation of two variables.

if x = 0 then y = 121
if x = 1 then y = 100
..
and so on...

Answer 20

whats wrong with drawing tool :) ??

Answer 21

there are infinite real pairs of x and y from real numbers satisfying the equation and we can find integer ones because we know that x,y<=121

Answer 22

Yes!

Answer 23

(x,y)=(121,0),(100,1),(81,4),(64,9),(49,16),(36,25)

Answer 24

But as the user said they x and y are real numbers : \((x,y) \in \mathbb{R}\)

So , x and y can have infinite values.

Answer 25

^that x and y are real numbers.

Answer 26

ahh, yes...infinite is answer :)

Answer 27

:)

Answer 28

@mukushla , if x and y are integer
there are 12 order pairs of (x,y) as solution, right ?

Answer 29

@RaDen yes, thats right...i did'nt write them because of symmetry.

Answer 30

is there any formula to find out all the real values of x and

Answer 31

and y