0:00
Hello.
00:01
So here the question says, the first question is that the sum of two numbers is seven.
00:06
Okay, we call the numbers a and b.
00:07
So then a plus b is going to be equal to seven.
00:10
And the sum of the squares of these two numbers is going to be 29.
00:15
So therefore, a squared plus b squared is 29.
00:17
Well, what we can do, we have two equations and two unknowns.
00:21
We can solve one of these for the other variable.
00:23
So if we solve the first equation for a, subtracting b, you get that a is going to be equal to, well, negative b plus seven or a is equal to seven minus b so if a is seven minus b well then we know that's seven minus b squared so seven minus b times seven minus b um plus b squared is equal to 29 well now we have an equation only one variable in it so therefore we can um distribute here you get seven times seven that's 49 and then we get negative 7b negative 7 b so that's going to be negative 14b, so minus 14b, and then negative b type negative b is going to be plus b squared, and then we have, again, plus b squared, is equal to 29.
01:11
Well, now we have b squared plus b squared.
01:13
It's going to be 2b squared.
01:14
So we can write this as 2b squared, and then we have the negative 14b, and then plus 49 is equal to 29.
01:23
Well, if we subtract 29 from both sides, we get 2b squared minus 14b, 49 minus 14b, 49, 29 is going to be, what, what's 49, 49 minus 29 is equal to 20, right? so we have 2b squared minus 14b, subtract 29 from both sides.
01:49
So plus 20 is then equal to zero.
01:52
Now we have a quadratic in standard form set equal to zero.
01:56
So we have a common factor of 2 we can pull out.
01:59
So we get two times b squared, two times negative seven.
02:05
So negative, not negative 14, two times negative seven, so negative seven b, right? and then plus 10 is equal to zero.
02:13
We can check this.
02:14
That's 2b squared minus 14b plus 20 equal to zero.
02:18
And then the inside can factor further, i believe.
02:21
We have two times, well, two times b squared minus 7b plus 10.
02:29
Well, five times two is going to be 10, right? so we can probably write this as two times b times b squared...