Question

Exercițiul 4 va rog frumos.

Answer 1

$\frac{ \sqrt{2} }{ \sqrt{2} - 1 } + \frac{2( \sqrt{2} - 1) }{ \sqrt{2} } = \frac{2 + \sqrt{2} }{ { \sqrt{2} }^{2} - 1 } + \frac{2( \sqrt{2} - 1) }{ \sqrt{2} } = \frac{2 + \sqrt{2} }{2 - 1} + \frac{2( \sqrt{2} - 1) }{ \sqrt{2} } = \frac{2 + \sqrt{2} }{1} + \frac{2( \sqrt{2} - 1) }{ \sqrt{2} } = 2 + \sqrt{2} + \frac{2( \sqrt{2} - 1) \sqrt{2} }{2} = 2 + \sqrt{2} + \frac{2 \sqrt{2}( \sqrt{2} - 1) }{2} = 2 + \sqrt{2} + \sqrt{2}( \sqrt{2} - 1) = 2 + \sqrt{2} + 2 - \sqrt{2} = (2 + 2) + ( \sqrt{2} - \sqrt{2}) = 4$

Answer 2

Răspuns

Explicație pas cu pas:

√2/(√2-1)+2(√2-1)/√2=4

√2(√2+1)/(√2-1)(√2+1)+2√2(√2-1)/(√2)²=4

(√2)²+√2)/(√2)²-(1)²+[2(√2)²-2√2]/2=4

(2+√2)/(2-1)+(2*2-2√2)/2=4

(2+√2)/1+(4-2√2)/2=4

[2(2+√2)+4-2√2)]/2=4

(4+2√2+4-2√2)/2=4

8/2=4

4=4