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)

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)

rational · Answer

@dan815

rational · Answer

@IrishBoy123

anonymous · Answer

use substitution

rational · Answer

$$\sqrt{x ^{2}+\sqrt{x ^{2}+11}}+\sqrt{x ^{2}-\sqrt{ x ^{2} +11}} = 4$$

Alright! substituting $\sqrt{x^2+11}=u~~\implies~~ x^2=u^2-11$

the equation then becomes
$$\sqrt{u^2+u-11}+\sqrt{u^2-u-11} = 4$$

anonymous · Answer

you still cant square both sides

anonymous · Answer

complete the square?

rational · Answer

im actually thinking of rationalising the left hand side expression

rational · Answer

but idk how useful it is..

rational · Answer

completing the square doesn't look that primising..

anonymous · Answer

you can try

dan815 · Answer

YOU'RE RATIONAL leave to me im irrational

anonymous · Answer

...

rational · Answer

you're more like complex/imaginary danny

rational · Answer

i gave up rationalising half way as it got really complicated

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

so there ought to be some trick

dan815 · Answer

ok i just expanded it

dan815 · Answer

is that easier to solve?

dan815 · Answer

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