au départ dire résoudre dans dans l ensemble C

please design a very hard problems

Note that, the given expression involving 'a' is symmetric in 'a' and thus, if 'k' is a root if the equation then '-k' is another root. sqrt(a) + sqrt(-a) = 12 => sqrt(a) + i*sqrt(a) = 12 => sqrt(a) * (1 + i) = 12 Squaring both sides, => 2ia = 144 => a = 72/i = -72i So, a = 72i is another solution. Ans. a = + or - 72i Note: To get the positive root analytically, in the LHS, take common sqrt(-a)

(rt3-1)/rt2 =(rt6-rt2)/2

First view 😊❤🎉

x√x=27 ; i,e x^3=729 ; i,e x°3-729=0 ; i,e ((x-9)(x^2+9x+81)= 0 ; i,e x=9 or x=[-9+√(81-324)])/2 or x= [-9-√(81-324)]/2 ; So, x=9 or x=[-9+√(-243)]/2 or x= [-9-√(-243)]/2 ; i,e x=9 or x=(-9+9√3i)/2 or x=(-9-9√3i)/2

7+3/7-3 = 10/4

Isse accha sabko cube root mai lete to asaan ho jata

m + n = 8, mn = 48 . * mn = 48 = 2x24 = 4x12 ** 12 - 4 = 8 = m + n *** m = 12, n = 4 m (-) n = 8./.

In fact, this problem solution serves to found numbers to factor a expression whit the form: x²±ax±b. Obviously, this is useful when ax and b are huge numbers

(3)^(1÷5)=?

3:38 missed dividing the Log base 5 of 2 by 2 4:44 started combining the two addends making 5 square but then corrected the Log base 5 of 2 leaving the 5 squared 5:32 fixed the previous errors during the combining of the two addends 5:40 error copying the base 5 making it base 3 5:48 treated the Log base 3 of 2 as the correct Log base 5 of 2 giving us the correct answer You always put wonderful videos out, these errors are exceptions not like the regular work produced. I appreciate the work you do putting out these videos regularly like you do. Thank you for putting them out and keeping me thinking.

2aa - 2bb = 98 * aa - bb = 49 49 = 24 + 25 = 25x25 - 24x24 = 625 - 576 *** a = 25 , b = 24 ./.

XX - YY = 36 *. 36 = 100 - 64 = 10x10 - 8x8 ** X = 10 , Y = 8./.

XX - Y = 43, YY - X = 43. * XX - Y = 43 = 49 - 6 = 7x7 - 6 ** YY - X = 43 = 36 + 7 = 36 -(-7) *** X = -7, Y = 6./.

aa - bb = 4, ab = 2 * aa - bb = 4 = 6,25 - 2,25 = (2,5x25)-(1,5x1,5) ** 2,5 + 1,5 = 4 = ab *** a = 2,5 ,b = 1,5./.

X + Y = 20, XY = 44 . * 44 = 2x22 = 4x11 22 - 2 = 20 = X + Y *** X = 22, Y = 2 ./.

aa - b = 31, bb - a = 31. *. aa - b = 31 = 36 - 5 = 6x6 - 5 ** bb - a = 31 = 25 -(-6) = 5x5 + 6 *** a = -6, b = 5./.

It's just two steps sum which has been made so difficult unnecessarily.

Nice 👍👍👍👍. Keep going

a=b . So, a = - b - 1 a = - a -1 2a = -1 a = -1÷2 And, b = -1÷2

i interpreted them as roots of a quadratic with a= 1 where the sum (x+y) = -b and product (xy) = c so i developed x² - 4x + 16 = 0 and found the roots by completing the square

Uhhhh so 14=14😂

What exactly are you solving here? Thumbnail was saying to solve for x. That answer would be x=4-y So why solve y?

Cant we solve it by comsidering them as hyperbola and straight line

Wait wait wait you can just divide or multiply by anything when you say its equal to 0? That makes everything so much easier!

Okay so I just tried to solved it, and my solution is either x is 0, or x is -8 Just to see if im right imma warch the video now

I really thought that the values will be real with some differnt approach😅

my honest reaction square both sides? me after seeing the video (aw hell nah)

Are German Olympiads this easy?

its just a basic simultaneous equation

Ok, I may have resolved this by calculating the square root instead of keeping it as it was like in the video

You could also just take the derivative of the function x^2-14x+14, it’s basic optimization, a topic in calculus I.

scary olympiad problem guys 😱 😱 there are letters instead of numbers1!1!1!!1 i hate math!1!!1!1!1!11!111!1

My brain just exploded itself

Use symmetry for faster solution. x=1+z, y=1-z, and (1+z)(1-z)=4 yield z^2=-3, z=±i√3, x=1±i√3, and y=1∓i√3

Wrong Answer.

2:07 - 2:14 missing parentheses caused a missed distribution of the 2 the numerator should have become 2(√5)-2 6:59 - 7:09 positive 4 became negative 4 during the correction of 2x to 4x 7:17 - 7:23 adding 4 to both sides to move it across the equal sign should have given us 9 (the 4x made the move becoming -4x properly) 9:28 failed to copy 5184 (instead wrote 518) 9:48 multiplied 5148 by 4 (though still showing 518) 10:14 corrected 518 to 5184 (thank you for the fix) Thank you for the work you did, I appreciate the effort producing these videos as regularly as you do

2×(6^(1/2)+10^(1/2))

His work is correct but one 3 is added.Not required. 36(6+√35)=9{24+4√35} =9{24+2√(2×5×7)}=3^2{√14+√10)^2} Ans is 3(√14+√10)

It's solve another too much easy method

3(√14 + √10)

Answer 3

actually the answer 3(root 14 + root 10)

Good explanation #essessbiieducation

What about the second root in [-1, 0]? It's not a full solution, though, logic of solving is interesting

in Russia we call it «The Monte Carlo method» or “sort through method”.

Шок задание с выпускного экзамена гарварда 2^x=4, если x={R}

2 в 32 =2 в 32, не благодарите