An algebra problem by Kazi Zareer

Algebra Level 2

X 2 + 4 X 2 = 4 X^2 + \frac{4}{X^2} = 4 .

If X > 0 X > 0 , what is X X ?


The answer is 1.41421356237.

Kazi Zareer by Kazi Zareer , 18, Bangladesh

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1 solution

x 2 + 4 x 2 = 4 x^{2} + \frac{4}{x^{2}} = 4
x 4 + 4 = 4 x 2 x^{4} + 4 = 4x^{2}
x 4 − 4 x 2 + 4 = 0 x^{4} - 4x^{2} + 4 = 0
( x 2 − 2 ) 2 = 0 (x^{2} - 2)^{2} = 0
x 2 − 2 = 0 x^{2} - 2 = 0
x 2 = 2 x^{2} = 2
x = 2 = 1.4142 x = \sqrt{2} = 1.4142


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