Question

Mulțimea soluției ecuației 4x la a 2=(8+4✓3)|7-4✓3|.
va rog!

Answer 1

$4x {}^{2} = (8 + 4 \sqrt{3} ) \times |7 - 4 \sqrt{3} | \\ 4x {}^{2} = (8 + 4 \sqrt{3} ) \times (7 - 4 \sqrt{3} ) \\ 8 \times 7 - 8 \times 4 \sqrt{3} + 4 \sqrt{3} \times 7 - 4 \sqrt{3} \times 4 \sqrt{3} \\ 4x {}^{2} = 56 - 32 \sqrt{3} + 28 \sqrt{3} - 48 \\ 4x {}^{2} = 8 - 32 \sqrt{3} + 28 \sqrt{3} \\ 4x {}^{2} = 8 - 4 \sqrt{3} \\ x1 = - \sqrt{2 - \sqrt{3} } \\ x2 = \sqrt{2 - \sqrt{3} }$