Only Smart Students Can Solve This Math Problem!

Ajouté : 2026-05-26

[00:00:00]Imagine you meet up something that looks like this. What are you supposed to do?

[00:00:04]All right. So, for the question like this, without wasting your time, you just say solutions.

[00:00:09]This is solution.

[00:00:11]And then you indicate that this is your equation one, while this is equation two.

[00:00:16]And when you indicate like that, you can get equation one or equation two. You make one of the variables the subject.

[00:00:23]Now, in my case, I'll pick equation two, that is x y is equal to a four.

[00:00:30]Now, this xy is equal to a four, I'm going to divide by x both sides. So, this is x, this and this will go. We shall y is equal to four over x like this, okay? I hope you're able to see. And this can be called equation uh equation three.

[00:00:53]Now, from this point, since we used equation two to make y the subject right here, we'll go back to equation one and substitute in place of y here, we substitute equation three.

[00:01:08]And that would be x plus four over x is equal to a one. Okay? So, now, from this point, you can now um multiply throughout by x because x is the denominator. So, we can say x I'll bring it here or this side, it's okay. You multiply x times x. This will give us x power two plus here it will be four x over x which is equal to one x or x.

[00:01:47]So, here, this and this will cancel out.

[00:01:49]You remain with x power two plus four which is equal to x. And then here, you group the I mean you you write it in standard form. That is x ^ 2 - x + 4 is equal to a zero.

[00:02:06]Now from this point we can use quadratic formula to solve.

[00:02:10]So this is how the quadratic formula looks like. Okay?

[00:02:16]This is the quadratic formula. Okay?

[00:02:20]So once we do this, we can now identify our A is right here, B, and C. So for A it is a a one.

[00:02:32]While B, the coefficient there is -1, C is a four.

[00:02:38]And when we get these, we can now substitute them.

[00:02:43]And when we substitute this is what we're getting.

[00:02:47]Here we're getting a negative for B we know that B is a negative one plus or minus square root over negative uh B I mean negative one which is a B -1^2 - 4 the A there is a one, C is a four everything over two the A is a one.

[00:03:12]We simplify we're getting a one plus or minus square root over one -16 over a two. So this will be one plus or minus square root over -15 over a two.

[00:03:29]This is what we got here.

[00:03:31]So the value of x is a one plus 15 i because this is a complex number. We don't have real solutions.

[00:03:45]And here we can say one minus square root of 15 i over two. So these are the two x values.

[00:03:56]Now, to get the y value we'll go back to the to to this step. Okay, this stage where we said y y is equal to four over x. So, that is y is equal to four over x.

[00:04:16]Now, at this point we just substitute, okay? Since we found the y value I mean the x values so we can simply say y is equal to four over one plus 15 i over a two. So, when x is equal to one plus square root of 15 i over two meaning y will be equal to four over one plus 15 i over two. So, here we can say y is equal to Okay, so when we work out things here we're getting eight over one plus square root of 15 i. This is a the value of y when x is equal to what we have right here.

[00:05:10]For this other one we can say y is equal to We write four of course this four and in place of x here we write one plus a Is it minus one minus 15 i over two.

[00:05:29]And this of course will give us a almost the same but the sign will just differ. Here it will be eight over one minus square root of 15 i. So, these are the two y values. Thank you and bye-bye.