China | Math Olympiad | A Nice Algebra Problem 👇

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[@satyadev3848]

nice👍

[@LaxmanKumar-yi4cv]

Great

[@harikishan1900]

Very good 👍

[@user-go5sy7mu6q]

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lovely explaination maam😊😊

[@Maheshkumar-cw6un]

Good Teaching skills

[@user-tc9cb8zh7b]

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[@harshpathak2359]

Hello ma'am,it's very good solution

[@aruntiwari5714]

A and B values are correct 💯

[@prollysine]

One term of this type of equation is positive and the other term is negative. It's easy to figure out the solution in your head, just like that, a=-9, b=8, let's test it , (-9)^2-8=81-8 , 81-8=73 , 8^2-(-9)=64-(-9) , 64+9=73 , Of course, guesswork won't be accepted in the exam...
If the equation is quadratic, we must get four different solutions...
a=b^2-73 , -> b^4 |+/-| k*b^3 -146b^2 -b +5256 = 0 , by faktoring , based on the previous ones let k=9,
b^4+9b^3 -9b^3--81b^2 -65b^2-585b +584b+5256=0 , -> b^3(b+9)-9b^2(b+9)-65b(b+9)+584(b+9)=0 , (b+9)(b^3-9b^2-65b+584)=0 ,
b+9=0 , b=-9 , a=b^2-73 , a=(-9)^2-73 , a=81-73 , a=8 , test , a=8 , b= -9 , 8^2-(-9)=64+9 , 64+9=73 , OK ,
(-9)^2-8=81-8 , 81-8=73 , OK , b^3-9b^2-65b+584=0 , (b-8)(b^2-b-73)=0 , b-8=0 , b=8 , a=b^2-73 , 64-73= -9 , a= -9 ,
b^2-1-73=0 , b=9.05862 , a=9.05862^2-73 , a=9.05862 , b=-8.05862 , a=(-8.05862)^2-73 , a=-8.05862 ,
the pairs of numbers are the same, test , 9.05862^2-9.05862=73 , vice versa , (-8.05862)^2-(-8.05862)=73 , OK ,
solu. per pair of numbers, | a=-9 , b=8 | , | a=8 , b=-9 | , | a=b=9.05862 | , | a=b= -8.05862 | ,

[@prollysine]

Thanks , it wasn't an easy task, but I figured it out.
You have very beautiful hands and painted nails.

[@ichdu6710]

other solution after 2:42:
with case 2 we found
a = -b -1
we replace a in equation 2 finding a quadratic equation with b² +b - 72 = 0
solving this quadratic equation with the standard formula
solution 1: b1 = +8 ---> a1= -9
solution 1: b2 = -9 ---> a2= +8
after that verification.
btw: please avoid in your next video saying the word 'right' after nearly every line and starting the next line with the word "now". this is quite annoying and stressful