Solving a 'Stanford' University entrance exam

Added: 2026-06-01

[00:00:01]Welcome to Smart Math. Today I'm trying to solve this math Olympic problem with a three different method. So, I'm trying to solve this with three different method. Let's find out the solution. As our equation is x - 7 whole square that is equals to 36.

[00:00:15]So, if I'm going to write equation is x - 7 whole square that is 36.

[00:00:22]So, if I'm applying the square square of difference formula square of difference in which a - b whole square that is equals to a square - 2ab and plus b square here.

[00:00:39]So, this is equals to x square - 2 into x into 7 + 7 square that is equals to 36 here.

[00:00:51]So, this is x square 14 of x plus this is 7 7s are 49 that is equals to 36 here. So, this is positive goes equal opposite sign negative.

[00:01:07]>> [snorts] >> So, we got the value of x square that is - 14 of x + 49 - 36 that is equals to zero here.

[00:01:19]So, the next step is if I'm here x square here x square - 14 of x this is plus 4 49 and - 36 become + 13 that is equals to zero here.

[00:01:37]So, if I I'm so this is 13 we got the factor of 13 is + 13 here. I'm I'm wrote here for - 14 + 1 is become 14 and - 14 of x plus one of x that is equals to minus 14 of x here.

[00:02:05]So, we got the value of x squared that is equals to minus uh minus 13 of 14 plus one.

[00:02:20]Hold on, this is not 13. This is This is just 13 and minus one here. So, this is 13 and minus one is become become minus 14 of x here.

[00:02:38]We got the factor here minus 13 of x minus x plus 13 that is equals to zero.

[00:02:46]So, if I'm trying to common here x x minus 13 is and minus one here common.

[00:02:55]This is x minus 13 that is equals to zero here.

[00:02:59]So, again I'm common x minus 13 x minus 13 x minus 13 and we got x minus one here that is equal to zero here.

[00:03:10]So, the next step is x minus 13 is equals to zero two factor and x minus one that is equals to zero. This is negative goes equal opposite sign mean positive. So, we got x that is 13 or this is negative goes equal opposite positive.

[00:03:30]x is one here.

[00:03:32]We got the value of x here.

[00:03:34]Now, another method prime.

[00:03:36]Now, I'm going to method number two which is x minus seven whole squared that is equals to 36. So, this is positive value goes equal opposite sign negative.

[00:03:48]x minus seven whole squared minus 36 that is equal to zero.

[00:03:55]Or I'm going to X minus seven whole square.

[00:03:59]This is 36 it becomes six square. It becomes 36 here.

[00:04:03]That is equal to zero.

[00:04:05]I'm using the identity of sum and difference here.

[00:04:10]This mean we got the value of a square minus b square formula that is equal to a minus b into a plus b bracket here.

[00:04:23]So, we got the value of here X minus seven X minus seven minus six into X minus seven plus six.

[00:04:37]So, that is equal to zero.

[00:04:39]This mean X minus minus minus and seven and six it become seven six it become minus 13 here.

[00:04:50]And this is X that is minus seven plus six is minus one here that is equal to zero here.

[00:04:56]So, we got X minus 13 is equal to zero.

[00:05:01]Or X minus one that is equal to zero here. This is negative goes equal to positive.

[00:05:07]We got the value of X that is equal to 13 here.

[00:05:13]Or I said that X that is equal to this negative goes equal to positive.

[00:05:17]X is equal to one here.

[00:05:19]So, I'm trying to method number three.

[00:05:23]So, the last method if I'm going to X minus 17 whole square and this is 13 it become uh six square here. So, if I'm trying to both side by square square root here.

[00:05:37]Square root here.

[00:05:39]Square and square root cancel square and square root cancel. So, we got X minus seven that is equal to plus minus six here.

[00:05:46]This mean X minus seven + 6 that is equal to 0.

[00:05:50]Or x - 7 - 6 that is equal to 0 here.

[00:05:55]So, x that is equal to - 1 that is equal to 0.

[00:06:01]Or I said x - 7 and 6 - 13 that is equal to 0.

[00:06:06]So, this is negative goes equal opposite positive.

[00:06:09]Positive here.

[00:06:11]We got the value of x that is equal to 1 here.

[00:06:16]Or x that is equal to 13 here.

[00:06:21]So, now let's verify it to put in main equation.

[00:06:25]Now, let's verify to put in main equation for x is equal to 1 here.

[00:06:33]For the main equation become 1 minus 7 whole square that is equal to 36 - 6 whole square that is equal to 36.

[00:06:43]So, this is 36 is equal to 36 here.

[00:06:49]Now, for x is equal to 13 here.

[00:06:56]So, 36 x 13 - 7 whole square is equal to 36.

[00:07:05]6 square is 36 here. 13 - 7 6 square 6 here 36 is equal to 36. So, thanks for watching. Keep like, share, and subscribe.