Question

$\frac{x}{2 \sqrt{5} - 3 \sqrt{2} } = \frac{2 \sqrt{5 +} 3 \sqrt{2} }{ \sqrt{2} }$
aflati x​

Answer 1

Explicație pas cu pas:

x / ( 2√5 - 3√2 ) = ( 2√5 + 3√2 ) / √2

x / ( 2√5 - 3√2 ) = [ √2( 2√5 + 3√2 ) / 2 ]

= x / ( 2√5 - 3√2 ) = ( 2√10 + 6 ) / 2

= x / ( 2√5 - 3√2 ) = 2( √10 + 3 ) / 2

= x / ( 2√5 - 3√2 ) = √10 + 3

x = √10( 2√5 - 3√2 ) + 3( 2√5 - 3√2 )

x = 2√50 - 3√20 + 6√5 - 9√2

x = 2 · 5√2 - 3 · 2√5 + 6√5 - 9√2

x = 10√2 - 6√5 + 6√5 - 9√2

= 10√2 - 9√2

= √2

50 I 2

25 I 5 ⇒ 5√2

5 I 5

1

20 I 2

10 I 2 ⇒ 2√5

5 I 5