Solving a 'Harvard' University entrance exam | Find c?

Added: 2026-06-01

[00:00:00]Hello everyone, welcome to solve this nice math Olympiad algebra problem. So here we have this is square root of c minus three divided by c minus three is equals to three and we solve this problem for all the values of c.

[00:00:14]So I hope so you like this method but if you have any other method in your mind so please don't hesitate to write this method into the comment section.

[00:00:22]And here we you know about that if we have a number that is a so we write it as square root of a multiplied by square root of a.

[00:00:34]According to this rule of radicals we write the c minus three as in the same pattern we write c minus three as square root of c minus three multiplied by square root of c minus three.

[00:00:47]So we replace this value in this case so that our given question statement is written as in this form. This is square root of c minus three divided by square root of c minus three multiplied by square root of c minus three and this whole equation is equals to three only.

[00:01:08]And further in the next step we have this is c minus three and this c minus three are cancelled out by each other and we get the remaining values are one divided by square root of c minus three and this whole equation is equals to three.

[00:01:24]And for further in the next step our target is to find the values of c so for this we move this c minus three square root to the right hand side and it will be written as one equals to three times of square root of c minus three. And now further in the next step we need to remove this square root sign and for this we apply squaring on both of the sides. And you very well know about that the square root of one becomes one and here we apply square separately on both of these two values and it will becomes three square into square root of c minus three and it's whole square.

[00:02:01]And further we have three square becomes nine. These two and this square root are gone and we get here c minus three and in the left hand side we have only one.

[00:02:12]And now in the next step we multiply this nine separately on both of these two values and it will be written as nine times of c minus nine times of three becomes here 27. So we move minus 27 into the left hand side and it will becomes one plus 27 equals to nine times of c.

[00:02:32]And further we have one plus 27 becomes 28 equals to nine times of c.

[00:02:39]And further we need to divide both of the sides by nine in order to find the values of c. So that we divide both of the sides by nine and this will becomes here this nine and this nine are gone and we will just get only one value of c and that is equals to 28 divided by nine.

[00:03:00]And in the next step we need to verify that is this value of m be the solution or is this value of m be the extraneous root?

[00:03:11]So for this we need to copy down given question statement here. So that our given question statement is for verification case we just copy down question statement here. It is square root of c minus three divided by c minus three is equals to three.

[00:03:35]So this is the our given question statement and here in this case we just substitute the value of c is equals to 28 over nine into the left hand side and we check its behavior. So when we put it here it will becomes 28 over nine minus 3 square root divided by 28 over 9 minus 3 is equals to 3 or not. This is the upper claim.

[00:04:02]So, here when we take the LCM of the numerator term, it will becomes here.

[00:04:07]So, the LCM of this term becomes 9 and we get here 28 minus 9 times 3 becomes 27. And in the same pattern, we also take the LCM of the denominator term and its LCM becomes and we get here 28 minus 27 and we check that is this equals to 3 or not.

[00:04:28]So, here we just simplify the term then we have 28 minus 27 becomes here 1 and we know that the square root of 9 becomes here 3. So, you see that here we have the fraction over fraction so that we move the fraction from denominator to the numerator. We just have reciprocal this fraction and we write it as this is 9 divided by 28 minus 27 is also becomes here 1 and this is equals to 3.

[00:04:56]And further, you see that this is 3 times 3 becomes here 9 and finally, we have 3 is equals to 3. This shows that the value C is equals to 28 over 9 is satisfied our given question statement and this is our final answer of this question. And thank you so much for watching this video. Please subscribe to my channel for more exciting videos.