Question

CAN ANYBODY SOLVE THIS QUESTION ??
NEED HELP!!!
The number of irrational solutions of the equation
\[\sqrt{x ^{2}+\sqrt{x ^{2}+11}}+\sqrt{x ^{2}-\sqrt{ x ^{2} +11}} = 4\]
is
a.) 0
b.)2
c.)4
d.)infinite
justify your answer with a proof.
(topic - quadratic equations)

Answer 1

@dan815

Answer 2

@IrishBoy123

Answer 3

use substitution

Answer 4

\[\sqrt{x ^{2}+\sqrt{x ^{2}+11}}+\sqrt{x ^{2}-\sqrt{ x ^{2} +11}} = 4\]

Alright! substituting \(\sqrt{x^2+11}=u~~\implies~~ x^2=u^2-11\)

the equation then becomes
\[\sqrt{u^2+u-11}+\sqrt{u^2-u-11} = 4\]

Answer 5

you still cant square both sides

Answer 6

complete the square?

Answer 7

im actually thinking of rationalising the left hand side expression

Answer 8

but idk how useful it is..

Answer 9

completing the square doesn't look that primising..

Answer 10

you can try

Answer 11

YOU'RE RATIONAL leave to me im irrational

Answer 12

...

Answer 13

you're more like complex/imaginary danny

Answer 14

i gave up rationalising half way as it got really complicated

Answer 15

what do i do now, haha. i dont even go to school.

Answer 16

we are supposed to solve these questions in less than 2 min -_-

Answer 17

so there ought to be some trick

Answer 18

ok i just expanded it

Answer 19

is that easier to solve?