Răspuns:
Bună,
[tex]a = \sqrt{7} - \sqrt{2} \\ b = \sqrt{7} + \sqrt{2} \\ \\ a) \frac{1}{a} + \frac{1}{b} = \\ \frac{1}{ \sqrt{7} - \sqrt{2} } + \frac{1}{ \sqrt{7} + \sqrt{2} } \\ = \frac{ \sqrt{7} + \sqrt{2} }{7 - 2} + \frac{ \sqrt{7 } - \sqrt{2} }{5} \\ = \frac{ \sqrt{7} + \sqrt{2} + \sqrt{7} - \sqrt{2} }{5} \\ = \frac{2 \sqrt{7} }{5} [/tex]
[tex] \frac{4}{5} < \frac{2 \sqrt{7} }{5} < \frac{6}{5} | \times {}^{2} \\ \frac{16}{25} < \frac{28}{25} < \frac{36}{25} | \times 25 \\ 16 < 28 < 36[/tex]
[tex]b)m.a = \frac{a + b}{2} \\ = \frac{ \sqrt{7} - \sqrt{2} + \sqrt{7} + \sqrt{2} }{2} \\ = \frac{2 \sqrt{7} }{2} \\ = \sqrt{7} [/tex]
[tex]c)(a - b) ^{2} = \\ ( \sqrt{7} - \sqrt{2} - ( \sqrt{7} + \sqrt{2} )) ^{2} \\ = ( \sqrt{7} - \sqrt{2} - \sqrt{7} - \sqrt{2} ) \\ = ( - 2 \sqrt{2} )^{2} \\ = 4 \times 2 \\ = 8[/tex]
Sper că te-am ajutat
