Question

x^6 - 10x^3 + 16 solve this algebra​

Answer 1

Answer:

your solution is as follows

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Step-by-step explanation:

$to \: find : \\ values \: of \: x \\ \\ given \: hexic \: equation \: is \\ x {}^{6} - 10x {}^{3} + 16 = 0 \\ (x {}^{3} ) {}^{2} - 10x {}^{3} + 16 = 0 \\ \\ let \: here \\ x {}^{3} = k \\ thus \: then \\ k {}^{2} - 10k + 16 = 0 \\ \\ k {}^{2} - 8k - 2k + 16 = 0 \\ k(k - 8) - 2(k - 8) = 0 \\ (k - 2)(k - 8) = 0 \\ \\ k = 2 \: \: \: or \: \: \: k = 8$

$thus \: then \: \: resubstituting \: \\ accordingly \\ we \: get \\ \\ x {}^{3} = 2 \: \: \: or \: \: \: x {}^{3} = 8 \\ x = \sqrt[3]{2} \: \: \: or \: \: \: x = 2$