Question

Se dau numerele : a=√128 •(1/√8-1/√32) si b=√2 + 1-√2/2-√2.Calculati a•b-√2

Answer 1

$a = \sqrt{128} \times ( \frac{1}{ \sqrt{8} } - \frac{1}{ \sqrt{32} } )$

$a = 8 \sqrt{2} \times ( \frac{1}{2 \sqrt{2} } - \frac{1}{4 \sqrt{2} } )$

$a = \frac{8 \sqrt{2} }{2 \sqrt{2} } - \frac{8 \sqrt{2} }{4 \sqrt{2} }$

$a = 4 - 2$

$a = 2$

$b = \sqrt{2} + 1 - \frac{ \sqrt{2} }{2} - \sqrt{2}$

$b = 1 - \frac{ \sqrt{2} }{2}$

$b = \frac{2 - \sqrt{2} }{2}$

$ab - \sqrt{2} = 2 \times \frac{2 - \sqrt{2} }{2} - \sqrt{2} = 2 - \sqrt{2} - \sqrt{2} = 2 - 2 \sqrt{2} = 2(1 - \sqrt{2} )$