Question

$\sqrt[4]{18 + 5x} + \sqrt[4]{64 - 5x} = 4$
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Answer 1

Ответ:

$\sqrt[4]{18 + 5x} = a \\ \sqrt[4]{64 - 5x} = b \\ 18 + 5x = {a}^{4} \\ 64 - 5x = b {}^{4} \\ 5x = {a}^{4} - 18 \\ 64 - {a}^{4} + 18 = {b}^{4} \\ {b}^{4} + {a}^{4} = 82 \\ \binom{ {b}^{4} + {a}^{4} = 82 }{a + b = 4} = \binom{{b}^{4} + {a}^{4} = 82 }{a = 4 - b} = \binom{{b}^{4} + {(4 - b)}^{4} = 82}{a = 4 - b} \\ {b}^{4} + (4 - b) {}^{4} = 82 \\ (a – b) ^{4}  = a {}^{4} – 4a {}^{3} b + 6a {}^{2} b {}^{2}  – 4ab {}^{3}  + b {4}^{?} \\ {b}^{4} + 256 - 256b + 96 {b}^{2} - 16 {b}^{3} + {b}^{4} = 82 \\ 2 {b}^{4} - 16 {b}^{3} + 96 {b}^{2} - 256b + 174 = 0$

b=3

x=(64-81)/5= -17/5