Solving Square Root Inequalities #2

[@abhijeetchatterjee4129]

Thanks a lot. This was great help. I was stuck for quite sometime. Keep uploading.

[@touhami3472]

sqrt(A)> B Case B D1 of validity A>=0 IN D1 ==> S1 Case B>=0 ==> D2 of validity A>B^2 IN D2 ==> S2 Threfore S= S1 U S2 Sqrt(A)+sqrt(B)0 Conditions: A>=0, B>=0 AND p^2>= A+B 4AB

[@rukhshonatulyaganova835]

Thank you for your understandable lesson!

[@mymatheducation]

Glad it was helpful! Thank you for watching!

[@YulinaGoto]

But you can't just square them like that, can you? Like -49. How do you know if you can square an inequality (w/o making it false, of course)?

[@mymatheducation]

We are not really squaring the inequalities, we are finding the roots (zeros) of the corresponding square root equation. These represent the "boundary" points where the inequality goes from being true to false or where it goes from less than zero to greater than zero or greater to less.

[@YuvrajSingh-rs9fd]

thats why we first find x>0 x-5>0 to ensure that both side are positive

[@touhami3472]

@@mymatheducation but why you find D: x>=1 , D: x>=0, x-5>=0 ? How this domain is useful ???

[@clementokala]

good day please sir can you do more videos in inequalities like √3-2x ≥x thanks

[@Seemi]

Thank you so much!!

[@mymatheducation]

You're welcome! Thanks for watching!

[@crystaljaims5707]

After squaring both sides, X+x-5

[@jayita1523]

I did not get why were you checking for wheather the value of x can be 10 because the domain is greater than or equal to one and also x=5 change the inequality to an equality? Can you please explain 🙏

[@theordinary8526]

i was looking for something like this 10 root sign 2 so like bigger number on left abd smaller on right -_-

[@the_syntax_sorcerer]

It should be 2

[@surinderkaur1011]

Hey.. solution to second equation say domain [1,5) that includes 2 as well. But if consider x=2 and solve sqrt(2-1) +3 = sqrt (1) + 3 = 1+3 = 4 > 2 But that is not true. So shouldn't the domain be [1,2) Please correct me if I am wrong.

[@mymatheducation]

The domain is actually X is greater than or equal to one. The solution is [1, 5). I'm not sure what the issue is as 4 is certainly greater than 2 so 4>2 is a true statement so 2 is part of the solution. Thanks for watching.

[@nafimohammad411]

4>2 is true Please recheck

[@ananashrabi3728]

Thank you sir.

[@mymatheducation]

Anan Ashrabi you are very welcome!

[@touhami3472]

How your DOMAIN is USEFUL ? You make calculus without mathematcal rules !!! For you : sqrt(x) < -5 has same solutions as x< 25 in D: x>=0 !!!