An Important mathematics for students!

Hello my friends and students,
hope you are all well.
In this video we are going to solve a nice exponential equation for the students of class x.
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[@annabanerjee5164]

Verified,
The roots satisfied with the original equation.
Thank you for solution!

[@DebdasBandyopadhyay-yq5jg]

Thanks for watching, welcome

[@daviddoby9648]

Équation (1):
X^(2/3)+ X^(1/3)=2
Let Y=X^(1/3)=³√X
(1) : [X^(1/3)]^2 + [X^(1/3)]=2
(1) Becomes :
(2) : Y^2 + Y -2 =0
Équation of the 2nd degree that we can solve easily :
1 is évident solution of (2)
So (2) is équivalent with (Y-1)(Y+2)=0
Two solutions, Y=-2 or Y=1
Or, using Delta
d=b²-4ac= 1²-4*1*(-2)=1+8=9
d >0 so 2 solutions
Y1=(-b-√d)/(2a)=(-1-√9)/2=(-1-3)/2=-4/2=-2.
Y2=(-b+√d)/(2a)=(-1+√9)/2=(-1+3)/2=2/2=1.
³√X=Y so X=Y³
X1=Y1^3=(-2)^3=-8
X2=Y2^3=1^3=1
Solution in R={1 ; -8}
So thé answer is X= {1 or -8}

[@DebdasBandyopadhyay-yq5jg]

Nice