00:00x x x x x plus x equal 10. What is x? Solution x x x x equal x power
00:133 x cube. So x cube plus x
00:19equal 10. Now x cube plus x minus 10 equal 0. x comes to left side and becomes negative. Now
00:3110 is
00:33equal to 8 plus 2. So we can write this x cube plus x minus 8 plus 2 equal 0.
00:44Okay so x cube plus
00:48x minus 8 minus 2 equal 0. Now x cube minus 8 plus x minus 2 equal 0. Why? Because
01:00I can make x cube
01:03minus 2 power 3 2 cube. So both are cubes. That's why I rearranged x cube and 8 together. So
01:11plus x
01:12minus 2 equal 0. Now x we have a formula. The formula is x cube minus y cube that is
01:25equal
01:25to x minus y x square plus x y plus y square. According to this formula x cube minus 2
01:39power
01:39cube. This we can write x minus 2 and x square y square sorry plus x y. So plus x
01:52is x but y
01:53is 2. So 2x this becomes x y plus y square. So y is 2 2 square. Okay and plus
02:02x minus 2 x minus
02:042 equal 0. Now how can we write x minus 2 and x square plus 2 x plus 4 this
02:16become and plus x minus 2
02:20equal 0. Now we can write x minus 2 and x square plus 2 x plus 4 plus this can
02:33we can write x minus 2
02:35multiply 1 equal 0. So x minus 2 and x minus 2 and this one and here 1. These are
02:50not common. So we can write
02:52x square plus 2 x plus 4 and plus 1. So common together. Common is just written once and those
03:02which are not
03:03common are written together. Equal 0. Now how you write. So x minus 2 and from this x square plus
03:142 x plus 5
03:16and this is 0. So we know that this 2 when you multiply become 0. It means either x minus
03:252 is equal to 0
03:28or x square plus 2 x minus sorry plus 5 equal to 0. Because you know the rule a multiply
03:38b is 0. So either a is 0
03:41either b is 0. This is the rule. Okay. So if you know this we can now solve both of
03:48the questions both of the
03:50equations. So let's say this is equation number 1. So from 1 you can write x minus 2 equals 0.
03:59So x become 2
04:01because 2 goes to the right side of the equation and it becomes plus 2. So x is equal to
04:092. This is the
04:10first solution. Now from the second equation what we can write number 2. We can write x square plus
04:20plus 2 x plus 5 equal to 0. What is this? This is quadratic equation. Yes. Quadratic equation.
04:32You may know this. We can solve this using various methods. I am using it using the formula. So what
04:39is the
04:40general form of quadratic equation? A x square plus b x plus c equal 0. So comparing both. We compare
04:49both.
04:49So we can see a is equal to 1. Because before x square there is nothing. So we say 1
04:56is there. So a is 1
04:58and b is equal to 2 and c is equal to 5. Yes. And what is the formula? Quadratic formula.
05:08So what is that
05:09formula? Quadratic formula. The formula says minus b plus minus b square minus 4 a c whole square root
05:19divide 2 a this equals x. So putting the values we have minus b b is 2. So minus 2
05:30plus minus and here
05:38divide 2 and 1. Yes. Now we have minus 2 plus minus. Minus 2 plus minus and 4 minus 20.
05:54Yes. 4 multiply 1 4 4 and then multiply
05:58to 5. That is 20. Okay. And divide 2. So what we get minus 2 plus minus and here minus
06:0916. Yes.
06:10And divide 2. So what we get now? From this you can write minus 2 plus minus and here is
06:1916 multiply minus 1.
06:21You can write it or minus 1 multiply 16. It is up to you. And like that and divide 2.
06:29Then what we get minus 2 plus minus.
06:33Here we can write separately 16 square root minus 1 square root divide 2. Now you know that minus 1
06:41square root
06:42is equal to iota is equal to iota. Okay. This is equal to iota. Okay. This is the imaginary number.
06:45Okay. This is the imaginary number. When the radical is negative. So you use the imaginary number or complex number.
06:51You can't use it by real numbers. So minus 2 plus minus 16 square root is 4 and minus 1
07:00square root is iota. So 4 iota divide 2. Now from the numerator you can say 2.
07:09So 2 is let's say 2 is let's say 2. Okay. We have 2 solutions minus 2 plus 4 iota
07:15or in other words you can just first simplify it. So 2 is taken as common. Yeah. Let's first separate
07:26this and then we solve minus 2 plus 4 iota divide 2 or this is x.
07:35And here also or x is equal to minus 2 minus 4 iota divide 2 because these are plus minus
07:42so I just separate it. Okay. Now I solve it. So let's say this is number 3 and this is
07:49number 4. So number 3. Number 3 gives us minus sorry x equals minus 2 minus 2 plus 4 iota
08:02divide 2.
08:04So 2 is taken as come. So 2 is taken as come. Let's say minus 2 is taken common. So
08:10this become minus 1 minus 2 iota divide by 2. So 2 to cancel and we have no minus 1
08:21plus 2 iota because just 2 is taken common. Okay.
08:23So we have no minus 1 plus 2. So we have no minus 1 plus 2. So we have no
08:26minus 1 plus 2 iota. This is our first solution from the quadratic equation. And now from 4. So what
08:35is 4? We write it there. Minus 2 minus 4 iota divide 2.
08:44So 2 to cancel. So 2 to cancel. So minus 1 minus 2 iota. That is x. Okay. So what
08:57are our solutions? Solution 2 are the complex solutions. And one solution is the x is equal to 2. This
09:06is the real solution.
09:08Okay. So one is real solution. And two are complex solutions.
