Question

Qual valor e cálculo de:

(√7 + √11)
________
√7 - √11)

Answer 1

racionalizar

$\frac{ \sqrt{7}+ \sqrt{11} }{ \sqrt{7}- \sqrt{11} } = \\ \\ \frac{( \sqrt{7}+ \sqrt{11})( \sqrt{7} + \sqrt{11}) }{( \sqrt{7} - \sqrt{11} )( \sqrt{7} - \sqrt{11}) } = \\ \\ \frac{( \sqrt{7} + \sqrt{11})^2 }{ \sqrt{7^2}- \sqrt{11^2} } = \\ \\ \frac{ \sqrt{7^2}+2. \sqrt{7} . \sqrt{11} + \sqrt{11^2} }{7-11} = \\ \\ \frac{7+2 \sqrt{77}+11 }{-4} = \\ \\ \frac{18+2 \sqrt{77} }{-4} = \frac{2(9+ \sqrt{77}) }{-4} =- \frac{(9+ \sqrt{77} }{2} = \frac{-9- \sqrt{77} }{2}$