Question

Exercitiul 8 plss !!…nu doar raspuns, si rezolvare, ma incurc la rezolvare am nevoie de totii pasii.!!!

Answer 1

Explicație pas cu pas:

a)

${( \sqrt{2}x + 1)}^{2} - 2(x + \sqrt{3})(x - \sqrt{3}) =$

$= {( \sqrt{2}x)}^{2} + 2 \cdot \sqrt{2}x \cdot 1 + {1}^{2} - 2( {x}^{2} - {( \sqrt{3} )}^{2})$

$= 2{x}^{2} + 2 \sqrt{2}x + 1 - 2({x}^{2} - 3)$

$= 2{x}^{2} + 2 \sqrt{2}x + 1 - 2{x}^{2} + 6$

$= 2 \sqrt{2}x + 7$

b)

${(x - \sqrt{3})}^{2} - (x + \sqrt{5})(x - \sqrt{5}) + \sqrt{3}(2x - 1) =$

$= ({x}^{2} - 2 \cdot x \cdot \sqrt{3} + {( \sqrt{3} )}^{2}) - ( {x}^{2} - {( \sqrt{5} )}^{2}) + 2\sqrt{3}x - \sqrt{3}$

$= {x}^{2} - 2\sqrt{3}x + 3 - {x}^{2} + 5 + 2\sqrt{3}x - \sqrt{3}$

$= 8 - \sqrt{3}$

c)

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

$= 2( {x}^{2} + 2 \cdot x \cdot \sqrt{2} + {( \sqrt{2} )}^{2}) - ({( \sqrt{2}x)}^{2} + 2 \cdot \sqrt{2}x \cdot 1 + {1}^{2} )$

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

$= 2{x}^{2} + 4\sqrt{2}x + 4 - {2x}^{2} - 2\sqrt{2}x - 1$

$= 2\sqrt{2}x + 3$

d)

$3 {(x - \sqrt{5} )}^{2} - ( \sqrt{3}x + 1)( \sqrt{3}x - 1) + 6 \sqrt{5}x =$

$= 3( {x}^{2} - 2 \cdot x \cdot \sqrt{5} + {( \sqrt{5}) }^{2}) - ( {( \sqrt{3}x)}^{2} - {1}^{2}) + 6 \sqrt{5}x$

$= 3{x}^{2} - 6 \sqrt{5}x + 3 \cdot 5 - (3 {x}^{2} - 1) + 6 \sqrt{5}x$

$= 3{x}^{2} - 6 \sqrt{5}x + 15 - 3 {x}^{2} + 1 + 6 \sqrt{5}x = 16$