Find all the real fourth roots of 256/2401

vogarsfN8

vogarsfN8

Answered question

2022-11-28

Find all the real fourth roots of 256 2401

Answer & Explanation

driwant9HB

driwant9HB

Beginner2022-11-29Added 11 answers

Finding the real roots of 256 2401 1 4
Let us write,
x = 256 2401 1 4 x 4 = 256 2401
On factorization of the given fraction, we can write
256 2401 = 16 49 2 = 4 7 4
Therefore,
x 4 = 4 7 4 x 4 - 4 7 4 = 0 x 2 - 4 7 2 x 2 + 4 7 2 = 0 a 2 - b 2 = a + b a - b x - 4 7 x + 4 7 x 2 + 16 49 = 0 x = 4 7 , - 4 7
x 4 = 4 7 4 x 4 - 4 7 4 = 0 x 2 - 4 7 2 x 2 + 4 7 2 = 0 a 2 - b 2 = a + b a - b x - 4 7 x + 4 7 x 2 + 16 49 = 0 x = 4 7 , - 4 7
Hence, the real fourth roots of 256 2401 is 4 7 & - 4 7

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