Zadanie 1 Oblicz wartość wyrażenia dla a= 2 - i y= 1 + . Wynik zapisz w postaci a + gdzie a,b ∈ W.... Question from @Pati199512

Pati199512 @Pati199512

January 2019 1 48 Report

Zadanie 1
Oblicz wartość wyrażenia dla a= 2 - $\sqrt{5}$ i y= 1 + $3\sqrt{5} }$ . Wynik zapisz w postaci a + $b\sqrt{5} }$ gdzie a,b ∈ W.

c) y: x
d) $\frac{2y - x}{2x + y}$

Zadanie 2
Oblicz wartość wyrażenia dla a= $\sqrt{3} - \sqrt{2}$ , b= $\sqrt{3} + \sqrt{2}$

b) $(a-b)^{2}$
c) $\frac{1}{a} + \frac{1}{b}$

janka1946 $\frac{1}{a} + \frac{1}{b} = \frac{a+b}{ab} \\ \frac{ \sqrt{3}- \sqrt{2} + \sqrt{3} + \sqrt{2} }{( \sqrt{3}- \sqrt{2}) ( \sqrt{3+ \sqrt{2} } ) } = \frac{2 \sqrt{3} }{3-2} =2 \sqrt{3} 

$ $x=2- \sqrt{5 } \\ y=1+3 \sqrt{5} \\ \frac{x}{y} = \frac{2- \sqrt{5} }{1+3 \sqrt{5} } * \frac{1-3 \sqrt{5} }{1-3 \sqrt{5} } = \frac{2-6 \sqrt{5}- \sqrt{5} -15 }{1- (3 \sqrt{5)} ^{2} } } = \frac{-14-7 \sqrt{5} }{1-45}= \frac{-14-7 \sqrt{5} }{-44} = \\ \frac{-14}{44} + \frac{7}{44} \sqrt{5}$

d) $2y-x=2(1+3 \sqrt{5} )-(2- \sqrt{5} )=7 \sqrt{5} 

2x-y=2(2- \sqrt{5} )+(1+3 \sqrt{5}) =5+ \sqrt{5} } 
 \\ \frac{2y-x}{2x-y} = \\
 \frac{7 \sqrt{5} }{5+ \sqrt{5} } * \frac{5- \sqrt{5} }{5- \sqrt{5} } = \frac{35 \sqrt{5}-35 }{20} \\ \\ =- \frac{7}{4} + \frac{7}{4} \sqrt{5} 


$ $zad,2 \\ (a-b)^{2} =( \sqrt{3} - \sqrt{2} - \sqrt{3} - \sqrt{2} =

 (-2 \sqrt{2}) ^{2}=8$ [tex ]

zad 3

[tex] \frac{1}{a} + \frac{1}{b} = \frac{a+b}{ab} \\ \frac{ \sqrt{3} - \sqrt{2} + \sqrt{3} + \sqrt{2} }{( \sqrt{3- \sqrt{2})( \sqrt{3+ \sqrt{2}) } } } = \frac{2 \sqrt{3} }{3-2} =2 \sqrt{3} [tex]

2 votes Thanks 1