great work

Great problem with fine solution method🎉

*x⁴ = -1*

Excellent

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@vijaymaths5483

18 күн бұрын

Thank you! 😃

Dear friend , your answer is wrong because X^4=MINUS 1 NOT +1 So the final answer should be -sqr root of 2 times i

@vijaymaths5483

22 күн бұрын

Please check once again 😀 X^4= 1/X^4, means if you put X =1 then 1/X^4 also becomes 1,so X^4 =1 only ( not negetive 1)👍

@backgammonmaster

22 күн бұрын

X^2+1/X^2=O multiply both sides by x^2 you get x^4=MINUS 1 .

@SidneiMV

17 күн бұрын

​@@vijaymaths5483 NO! x⁴ + 1/x⁴ = -2

@SidneiMV

17 күн бұрын

​@@vijaymaths5483if x = 1 then x - 1/x = 0 BUT x - 1/x = i√2 so it's a HUGE MISTAKE saying x = 1 (the truth is x⁴ = -1)

x-1/x=√2i x²-√2ix-1=0 x=(√2i±√(-2-4.1.-1))/2 x=(√2i±√2)/2 |x|=1 Euler's formula: e^iθ = cosθ + i sinθ x=e^(i7π/4) or e^(i5π/4) (from the argand diagram, but you can solve cosθ+isinθ) 2π=8π/4 1087*7 = 1 mod 8 and 1087*5 = 3 mod 8 x¹⁰⁸⁷=e^(iπ/4) or e^(i3π/4) or (√2/2)*(±1+i) for (√2/2)*(+1+i) x¹⁰⁸⁷-1/x¹⁰⁸⁷=(√2/2)*(1+i)-1(1-i)/(√2/2)*(1+i)(1-i) (mult second part by (1-i)/(1-i)) =(√2/2)*(1+i) - (1-i)*(√2/2) = √2i for (√2/2)*(-1+i) x¹⁰⁸⁷-1/x¹⁰⁸⁷=(√2/2)*(-1+i)-1(-1-i)/(√2/2)*(-1-i)(-1+i) (mult second part by (-1-i)/(-1-i)) =(√2/2)*(-1+i) - (-1-i)*(√2/2) = √2i Ans= √2i

ｘ^4＝ー１だよ。だから答えは ー(√２}i だ。間違っているから訂正してね

@vijaymaths5483

22 күн бұрын

No, X = 1 ( not negetive 1) Please check once again if you doubt about negetive 1. Thanks for watching and sharing your valuable feedback 🌺

@backgammonmaster

22 күн бұрын

@@vijaymaths5483 X is NOT=1

@dragoncat16

21 күн бұрын

@@vijaymaths5483 Solving the first equation for x you get x=(i+/-1)/sqrt(2) and that means x^4 = -1. From that, you get -sqrt(2)i for the answer (for either option).

@gaiatetuya92

21 күн бұрын

@@vijaymaths5483 貴方の解答が明らかに間違っているのだからそれを素直に認め訂正するのが常識です。貴方自身とチャンネルの信用のためにも。

@SidneiMV

17 күн бұрын

​@@vijaymaths5483X is NOT equal to 1! *x⁴ = -1*

答えが間違っている。チャンネルの信用が無くならないうちに訂正お願いします。

*HUGE MISTAKE HERE!* *x is NOT = 1* and x⁴ = -1 if x = 1 then x - 1/x = 0 but x - 1/x = i√2 *HUGE MISTAKE*

x - 1/x = i√2 find x²⁰⁸⁷ - 1/x²⁰⁸⁷ (x - 1/x)² = x² + 1/x² - 2 = -2 x² + 1/x² = 0 => *x⁴ = -1* (x² + 1/x²)(x - 1/x) = x³ - 1/x³ - (x - 1/x) = 0 *x³ - 1/x³ = i√2* 2087 = 2084 + 3 = (4)521 + 3 x²⁰⁸⁴ = (x⁴)⁵²¹ = (-1)⁵²¹ = -1 x²⁰⁸⁷ = -x³ x²⁰⁸⁷ - 1/x²⁰⁸⁷ = x²⁰⁸⁴x³ - 1/(x²⁰⁸⁴x³) = - (x³ - 1/x³) = *-i√2*