Solving a 'Stanford' University entrance exam | t=?

[00:00:00]Hello Friends find the value of 't' If t^2/36=36/t^2 let's have a solution since 36=6x6=6^2 then It will be t^2/6^2=6^2/t^2 by cross multiplication, we have t^2xt^2=6^2x6^2 bases same, powers add t^4=6^4 since 2+2=4, as 2x2=4 so we can write it as (t^2)^2=(6^2)^2 (t^2)^2-(6^2)^2=0 by this, we know the formula of a^2-b^2=(a+b)(a-b) It will be (t^2+6^2)(t^2-6^2)=0 we have two cases here case I is t^2+6^2=0 and case II is t^2-6^2=0 from case I, t^2=-6^2 take square root on both sides, √t^2=√-6^2 t=±6√-1 √-1=i then t=±6i so we have solution t=6i, t=-6i case II t^2-6^2=0 (t+6)(t-6)=0 either t+6=0 or t-6=0 t=-6, t=6 we have four solutions here, t1=6, t2=-6, t3=6i, t4=-6i in the next step, I'm going to verify t^2/36=36/t^2 take t=6 then 6^2/36=36/6^2 36/36=36/36 where 36 cancels 1=1 L.H.S=R.H.S t=-6 then (-6)^2/36=36/(-6)^2 36/36=36/36 36 cancels 1=1, L.H.S=R.H.S t=6i then (6i)^2/36=36/(6i)^2 6^2xi^2/36=36/6^2xi^2 as i^2=-1 from complex numbers so It will be 36x(-1)/36=36/36x(-1) where 36 and 36 cancels -1=-1, L.H.S=R.H.S t=-6i then (-6i)^2/36=36/(-6i)^2 6^2xi^2/36=36/6^2xi^2 It will be 36x(-1)/36=36/36x(-1) where 36 and 36 cancels -1=-1, L.H.S=R.H.S which shows that t=6, -6, 6i, -6i satisfies this equation of t^2/36=36/t^2 thanks for watching this video please subscribe this channel to get the notification of my new videos ok bye