Question

Help

Answer 1

Simultaneous equations

Answer 2

\[\huge \sqrt{a}+b=7\]
\[\huge \sqrt{b}+a=11\]

Answer 3

Solve for a and b

Answer 4

Each time i try with a different method i get different answers

Answer 5

not sure whthert there is a shortcut,
but the long way to do is by using elimination

Answer 6

a= (7-b)^2
plug it in 2nd equation

then square it,
you will get a 4th degree polynomial in 'b'
that gives you 4 values of b

Answer 7

I tried it , i am getting a quadratic how do i put it under the root :0

Answer 8

there are two whole number sollutions for this

Answer 9

sqrt b = 11 - (7-b)^2

square it now

Answer 10

one more thing i tried is to find the ratio between a and b yes wait

Answer 11

b = 11 -49-14b+b^2

Answer 12

a= 9, b =4
easy to eyeball

Answer 13

yeah , the question says that no trial and error :)

Answer 14

b = 11 -49-14b+b^2 <<<incorrect

Answer 15

still incorrect :P

Answer 16

b= (11- (7-b)^2)^2

Answer 17

Ok i didn't see the root forget it

Answer 18

so 4th degree plynimial creeping there

Answer 19

i don't know if it helps but
i got 5/3 = a/b

Answer 20

thats incorrect, right ?
given that one of the solution is 9,4

Answer 21

checked it again getting the same thing

Answer 22

maybe beacuse there is a root so extra sollution

Answer 23

i really don't know

Answer 24

I multiplied 1 st equation by a
second by b

Answer 25

and subtracted

Answer 26

argh silly mistakes i am making tdae

Answer 27

the first step is the culprit

Answer 28

lets think of a different approach....or solve that duadric eq.

Answer 29

*quadric

Answer 30

there must be a different approach to this

Answer 31

a and b must be perfect squares

b must be less than 7

which gives b must be 1 or 4

b=1, makes a imperfect square

Answer 32

great !

Answer 33

provided a and b are real