This algebra math challenge stumps everyone!

Añadido: 2026-05-25

[00:00:00]This is very tricky but very easy.

[00:00:02]Welcome back to my channel. First we are going to transfer this to the other side of the equation.

[00:00:09]So we will have x ^ 4 - x -1 ^ 4 is = 0.

[00:00:19]Now this can be expressed as x^ 2 ^ 2 - this will be x -1 raised to the power of 2 raised to the power of 2 again. So why am I not using this rais^ 2 is equal to zero. All right. Now we have difference of two squares here.

[00:00:48]Remember that a squ - b 2 is equal to a - b * a + b.

[00:01:00]Now in this case our a is x² and our b is x - 1 2 Moving forward, we have this will now be x^2 - x - 1 2 * x 2 + x - 1 2.

[00:01:56]All right, everything is equal to z.

[00:02:04]Now remember that a - b all 2 is equal to a 2 - 2 a b + b 2.

[00:02:19]So that means that we will write this as x^2 - this will be x^2 - 2x + 1 all 2 multiplied by x^2 + the same thing right?

[00:02:42]Oh, what am I doing? All squared. Not spreading anymore. We have opened the bracket. Okay. Then plus x² - 2x + 1 is equal to z.

[00:02:56]So let's open this bracket because of this negative sign. We have x^2 - x^2 - becomes plus 2x - plus is minus. If this is the first time you are seeing this lovely channel, please hit the subscription button, turn on your notification bell so that you don't miss our videos. We upload our videos as often as possible. Turn out your convenience. It must be something new for you to watch by God's grace.

[00:03:25]Okay. Thank you very much. Now, moving forward, this will be multiplied by x².

[00:03:38]Okay, we have x^2 + x 2 that is 2 x^2 - 2x + 1 is = 0. So if we solve this further x^2 x^2 is gone right and we left with 2x - 1 * 2x^2 - 2x + 1 is = 0. Now at this point remember that when you say a * b is equal to z. This implies that either a is equal to z or b is equal to z that is the truth.

[00:04:26]So that means that looking at this we will say that 2x - 1 is = 0.

[00:04:38]or 2x^2 - 2x + 1 is = 0. So from here we have 2x = 1. If this crosses the equal sign, so we have we divide both sides by two, right?

[00:04:57]We have x is equal to half. So this is the first um value of our x.

[00:05:04]Now looking at this one, we are going to use the quadratic equation formula to solve it. Now the quadratic equation formula states that x is equal to minus b plus or minus square roo<unk> of b ^ 2 - 4 a c everything / 2 a. Now in this case our a is 2, right? Our b is -2, our c is 1. So we are going to substitute this into the equation.

[00:05:42]So we have x = - - 2 + or - the<unk> of - 2 - 4 * 2 * 1 / 2 * 2. So we have x is - is plus. So we have 2 + or minus the square root of - 2 2 is 4 - 8 divided by two.

[00:06:21]So solving further we have x = 2 plus or minus<unk> -4 / okay this 2 * 2 which is 4 / 4. So we have x is 2 plus or minus square roo<unk> of 4 * -1.

[00:06:44]All right. So it's now roo<unk> of 4 * roo<unk> of -1 / 4. So x will be 2 + or - 2 root of -1 is i / 4.

[00:07:05]Okay. So now we have x 2 3 is equal to 2 / 4 + or minus 2 i / 4. So x to 3 is this divided by this will give us 1 / 2 plus or minus i / 2.

[00:07:29]Therefore the second and the third value of our x will be 1 + or minus i / 2.

[00:07:37]Thanks so much for watching and see you in my next video. Bye.