Okay, so this program we want Thio find the extreme values for T equals to 25 x square plus 25 y square Inside the region X squared plus y squared minus X one prospects y less so equals to one. Okay, so first we consider the imperial this region So, uh, passionate narrative off key our 50 x in the 50 wide. So the only critical points X equals two. Why put zero, which is inside the region. So at this point, p equals zero. Now we can see the boundary case. So on the boundary we considered a constraint equation geek Also x squared plus y squared plus x y minus one. We use the ground multiplier method Breaking off t equals to land that greater G So we have 50 X equals two Lambda times two x plus y And 50 Why it goes to learn that time to white plastics. Okay, so we use equation one. Subtract equation too. We have 50 x minus y It was two Lambda times X minus one. Okay, so we have two different cases. Case one is X equals toe. Why? So if X equals two why we parted this result into the constraint equation. Then we have three X squared equals toe one X equals two plus minus. Root off 3/3. So we have two points p one in close to 3/3 through two or 3/3 P two equals thio minus root on 3/3 minus root on 3/3 on the for both points for both points. Okay, for both points, P equals two ah, 50 times winter. So it's 50 over three and we have another case kiss to is if X is no equals to what that means, we can cancel all these two terms that gives us Lambda goes to 50. Yes, Ive lambda equals to 50. You plug it back to equation one. So we have 50 x equals toe 100 X plus 50 wide. That means X equals minus one. Then we use this and then the constraint equation. We have X equals two plus minus one. So we have two more points. So p three equals to one hour minus one before equals toe one minus 11 And for both points, the function t close to 50. So our conclusion is Um, yeah. This T courses here is the minimum value, and the T close to 50 is the maximum value. And this one, it could be a set of point set of point because it's not a maximum amendment touch, Yeah.