Only 1 Can Find a and b Harvard Interview Question Hardest Olympiad

In this video, let us find the value of and given that you have square + + = 10, b² + + = 20. Then let's have it be solution. Now from here we have a² + + a= 10. Then let's factor from here. we factor it out since it is common. square by here will be / here will be / will be + = 10. So let name this equation three. Then also we have b² + + = 20. Let's factor from here square by here is Then from here / here is / will be 1. Then equals 20. Then let us rearrange this expression. Arranging this one we have + + 1 = 20. Let's name this equation four. Now from here let's divide equation four by sorry equation three by equation four. So what we're going to have will be * + + 1 over * + + 1 = 10 / 20. So from here this we cancel out this they are the same. So we have / equals here is 1 here is 2. So we have here to be 1 / 2. Then from here we have to cross multiply we have 2 = meaning we have our to be equals 2 Then let us recall from equation one where we have a² + + = 10. Let's substitute the value of that = 2 From here we have a² + * 2 + = 10. So from here we have a² this will be 2 a² + = 10. So from here we have 3 a² + = 10. So now from here let us take this 10 here we have 3 a² + - 10 = and this is what we call quadratic. So to solve this quadratic use factorialization method we have the product to be equals minus 30 then our sum equals 1. Then they have two factors to be six then - 5. So from here we have we're going to have this to be 3 a² + 6 then - 5 - 10 equals So from here we're going to have this as 3 a² + 6 have 5 + 10 = 0. So what is common between this is 3 this will be + 2 6 / 3 what is common here is 5 here will be + 2 = so we have + 2 in common we can factor it out to be + 2 this by this will be 3 - 5 = by applying zero product rule. So we're going to have + 2 = 0 or 3 - 5 to be= So from here from here we have to be= -2. So we can have this as a1 = -2. Then we have 3 = 5 / 2 by 3. So we have a2 to = 5 / 3. So now from here we have to recall from where we have our to be equals 2 Then if our b= 2 definitely we are going to have b1 * 2 our a1 will be -2 then our b1 be equals -4 then likewise we have to be equals 2 Then our A2 equals 5 / 3. So definitely B2 be = 2 * A2. Then B2 2 * 5 / 3. So we have b2 to be equ= 10 / 3. So finally we can have a1 comma b1 to be equals a1 comma b1 = - 2 - 4. Then a2 comma b2 to be equals 5 / 3 comma / 3. So to check this to check this we have to recall a² + + = 10. For the first one that we have here will be square. You know we have comma to be = -2 - 4. So from here this will be -2² then -2 * this -4 here will be -2 then this is going to give us 10 here this negative will be affected by this power two here will be four then this minus and plus will be plus here will be 2 * 4 is 8 then - 2 is going to give us 10. Now we have 8 - 2 is 6. 4 + 6 = 10. So 10 equals 10. This satisfy. So if you also test for the second equation where we have b² + + = 20. Here will be -4 2 then -2 * -4 then -4 is going to give us 20. Now so from here we have this to be 16. Then this will be + 8 - 4 is going to give us 20. But we have 16. 8 - 4 is 4 which equals 20. So 20 = 20. And so therefore so therefore one can declare that comma that we have it to be - 2 - 4 is correct. Then to also check to also check for the second one. So you can check that one and make your comment in the comment section below.