Question

1/5v2+4v3 - 1/3v2+2v3 - 10/4v3+3v2
$\geqslant$
​

Answer 1

Răspuns:

$\large\bf\purple{\underline{3 \sqrt{2} - 3 \sqrt{3} }}$

Explicație pas cu pas:

$\bf{ \frac{1}{5 \sqrt{2} + 4 \sqrt{3} } - \frac{1}{3 \sqrt{2} + 2 \sqrt{3} } - \frac{10}{4 \sqrt{3} + 3 \sqrt{2} } = \frac{3(5 \sqrt{2} - 4 \sqrt{3} ) - (3 \sqrt{2} - 2 \sqrt{3}) - 2(4 \sqrt{3} - 3 \sqrt{2} )}{6} = }$

$\bf{ \frac{15 \sqrt{2} - 12 \sqrt{3} - 3 \sqrt{2} + 2 \sqrt{3} - 8 \sqrt{3} + 6 \sqrt{2} }{6} = \frac{18 \sqrt{2} - 18 \sqrt{3} }{6} = \frac{6(3 \sqrt{2} - 3 \sqrt{3}) }{6} =\large\bf\purple{\underline{3 \sqrt{2} - 3 \sqrt{3} }} }$