Explicație pas cu pas:
a = (4/√3 - 7/√2)*√6 + |12 - 7√3|
b = √(6² + 8²) - 8/√2
a) 12 < 7√3 => |12 - 7√3| = 7√3 - 12
[tex]a = \left( \frac{4}{ \sqrt{3}} - \frac{7}{ \sqrt{2}}\right) \times \sqrt{6} + |12 - 7 \sqrt{3} | \\ = \frac{4 \sqrt{6} }{ \sqrt{3} } - \frac{7 \sqrt{6} }{\sqrt{2} } + 7 \sqrt{3} - 12 \\ = 4 \sqrt{2} - 7 \sqrt{3} + 7 \sqrt{3} - 12 \\ = 4 \sqrt{2} - 12 = 4( \sqrt{2} - 3)[/tex]
b)
[tex]b = \sqrt{ {6}^{2} + {8}^{2} } - \frac{8}{ \sqrt{2} } = \sqrt{36 + 64} - \frac{8 \sqrt{2} }{2} \\ = \sqrt{100} - 4 \sqrt{2} = 10 - 4 \sqrt{2} [/tex]
[tex]a + b = 4 \sqrt{2} - 12 + 10 - 4 \sqrt{2} = - 2 \\ [/tex]
[tex]{(a + b)}^{10} = {( - 2)}^{10} = {2}^{10} = 1024\\ [/tex]
