Solving a 'Stanford' University entrance exam | t=?
Asad International Academy
[{'start': '0.000', 'end': '2.000', 'text': 'Hello Friends'}, {'start': '2.000', 'end': '4.998', 'text': "find the value of 't' If"}, {'start': '4.998', 'end': '9.589', 'text': 't^2-t^3=36'}, {'start': '9.589', 'end': '14.095', 'text': "let's have a solution"}, {'start': '14.095', 'end': '16.428', 'text': 'It can be written as'}, {'start': '16.428', 'end': '27.027', 'text': 't^2-t^3-36=0'}, {'start': '27.027', 'end': '41.508', 'text': "t^2-t^3-9-27=0 since '-36' is same as '9-27'"}, {'start': '41.508', 'end': '44.672', 'text': 'by corresponding'}, {'start': '44.672', 'end': '60.176', 'text': "t^2-t^3-3^2-3^3=0 since '9' is same as '3^2' and '27' is same '3^3'"}, {'start': '60.176', 'end': '61.758', 'text': 'as you can see here'}, {'start': '61.758', 'end': '64.784', 'text': 't^2 and 3^2'}, {'start': '64.784', 'end': '68.468', 'text': 't^3 and 3^3'}, {'start': '68.468', 'end': '70.956', 'text': 'we can write it as'}, {'start': '70.956', 'end': '84.208', 'text': 't^2-3^2-t^3-3^3=0'}, {'start': '84.208', 'end': '99.451', 'text': '(t^2-3^2)+(t^3+3^3)=0'}, {'start': '99.451', 'end': '114.483', 'text': 'we know the formula of a^2-b^2=(a+b)(a-b) for (t^2-3^2)'}, {'start': '114.483', 'end': '133.411', 'text': 'and here we know the formula a^3+b^3=(a+b)(a^2-ab+b^2) for (t^3+3^3)'}, {'start': '133.411', 'end': '137.994', 'text': 'then It will be'}, {'start': '137.994', 'end': '162.535', 'text': '(t+3)(t-3)-(t+3)(t^2-3t+3^2)=0'}, {'start': '162.535', 'end': '167.567', 'text': 'here (t+3) can be common'}, {'start': '167.567', 'end': '188.003', 'text': '(t+3)[(t-3)-(t^2-3t+9)]=0'}, {'start': '188.003', 'end': '208.074', 'text': '(t+3)[t-3-t^2+3t-9]=0'}, {'start': '208.074', 'end': '226.901', 'text': '(t+3)(-t^2+4t-12)=0'}, {'start': '226.901', 'end': '230.345', 'text': 'we have two cases here'}, {'start': '230.345', 'end': '237.785', 'text': 'case I is t+3=0'}, {'start': '237.785', 'end': '250.665', 'text': 'and case II is -t^2+4t-12=0'}, {'start': '250.665', 'end': '268.682', 'text': "from case I 't=-3' which is the value of 't', our first real solution"}, {'start': '268.682', 'end': '271.850', 'text': 'and from case II, -t^2+4t-12=0'}, {'start': '271.850', 'end': '276.726', 'text': 'divide it by (-1) on both sides'}, {'start': '276.726', 'end': '289.052', 'text': 'we have t^2-4t+12=0'}, {'start': '289.052', 'end': '298.785', 'text': 'which is like quadratic equation ax^2+bx+c=0'}, {'start': '298.785', 'end': '309.452', 'text': 'by corresponding, a=1, b=-4, c=12'}, {'start': '309.452', 'end': '330.039', 'text': 'apply now quadratic formula t=-b±√b^2-4ac/2a'}, {'start': '330.039', 'end': '332.929', 'text': "I'm going to put the values here"}, {'start': '332.929', 'end': '353.916', 'text': 't=-(-4)±√(-4)^2-4(1)(12)/2(1)'}, {'start': '353.916', 'end': '356.686', 'text': 'simplify this'}, {'start': '356.686', 'end': '375.648', 'text': 't=4±√16-48/2'}, {'start': '375.648', 'end': '388.068', 'text': 't=4±√-32/2'}, {'start': '388.068', 'end': '402.063', 'text': 't=4±√16x2x-1/2'}, {'start': '402.063', 'end': '416.402', 'text': 't=4±√16x√2x√-1/2'}, {'start': '416.402', 'end': '423.454', 'text': "where '√-1=i' from complex numbers"}, {'start': '423.454', 'end': '424.851', 'text': 'then we have'}, {'start': '424.851', 'end': '441.403', 'text': 't=4±4√2i/2'}, {'start': '441.403', 'end': '444.972', 'text': '2 can be common'}, {'start': '444.972', 'end': '450.508', 'text': 't=2(2±2√2i)/2'}, {'start': '450.508', 'end': '452.508', 'text': '2 and 2 cancels'}, {'start': '452.508', 'end': '459.049', 'text': 't=2±2√2i'}, {'start': '459.049', 'end': '472.444', 'text': "which is also the value of 't', our complex solution"}, {'start': '472.444', 'end': '474.281', 'text': 'three solutions here'}, {'start': '474.281', 'end': '493.929', 'text': 't1=-3, t2=2+2√2i, t3=2-2√2i'}, {'start': '493.929', 'end': '502.496', 'text': "in the next step, I'm going to verify"}, {'start': '502.496', 'end': '509.245', 'text': 't^2-t^3=36'}, {'start': '509.245', 'end': '513.841', 'text': "put the value of 't=-3'"}, {'start': '513.841', 'end': '525.336', 'text': '(-3)^2-(-3)^3=36'}, {'start': '525.336', 'end': '540.234', 'text': '+9-(-27)=36'}, {'start': '540.234', 'end': '550.762', 'text': '9+27=36'}, {'start': '550.762', 'end': '558.549', 'text': '36=36'}, {'start': '558.549', 'end': '564.631', 'text': 'L.H.S=R.H.S'}, {'start': '564.631', 'end': '576.792', 'text': 'which shows the values of t1=-3, t2=2+2√2i and t3=2-2√2i'}, {'start': '576.792', 'end': '585.936', 'text': "satisfies the equation of 't^2-t^3=36'"}, {'start': '585.936', 'end': '588.685', 'text': 'thanks for watching this video'}, {'start': '588.685', 'end': '593.384', 'text': 'please subscribe this channel to get the notification of my new videos'}, {'start': '593.384', 'end': '601.604', 'text': "and don't forget to share these videos with your classmates and friends so that they also have a benefit of it"}, {'start': '601.604', 'end': '607.216', 'text': 'you can also visit the 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