Question

A Calculati :
a)2(x-3)(x+3)-(√2x+3)^2+√72x
b) (x+5)^2+(x-1)2-(√2x+4)(√2x-4)
c) (2x-3)^2-4(x-√2)(x+√2)

B Descompuneti in factori:
a) (x-√3)^2-48
b) (√2x-3)^2-32x^2
c) (x^2+2x-3)^2-(x-1)^2

Answer 1

Explicație pas cu pas:

A

a )

2( x - 3 )( x + 3 ) - ( √2x + 3 )² + √7=

2( x² - 9 ) - ( 2x + 6√2x + 9 ) + 6√2x

= 2x² - 18 - 2x - 6√2x - 9 + 6√2x

= 2x² - 18 - 2x - 9

= 2x² - 27 - 2x

72 I 2

36 I 2

18 I 2  ⇒ 6√2

9 I 3

3 I 3

1

b )

( x + 5 )² + ( x - 1 ) · 2 - ( √2x + 4 )( √2x - 4 ) =

= ( x + 5 )² + 2x - 2 - ( 2x - 16 )

= ( x + 5 )² + 2x - 2 - 2x + 16

= ( x + 5 ) ² - 2 + 16

= ( x² + 2 · x · 5 + 5² ) - 2 + 16

= ( x² + 10x + 25 ) - 2 + 16

= x² + 10x + 25  - 2 + 16

= x² + 10x + 39

c )

( 2x - 3 )² - 4( x - √2 )( x + √2 ) =

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

= ( 2x - 3 - 2√x² - 2 )( 2x - 3 + 2√( x - √2 )( x + √2 )

= ( 2x - 3 - 2√x² - 2 )( 2x - 3 + 2√x² - 2 )

B

a )

( x - √3 )² - 48 =

= ( x - √3 - √48 )( x - √3 + √48 )

= ( x - √3 - 4√3 )( x - √3 + 4√3 )

= ( x - 5√3 )( x + 3√3 )

48 I 2

24 I 2

12 I 2  ⇒ 4√3

6 I 2

3 I 3

1

b )

( √2x - 3 )² - 32x² =

= ( √2√x - 3 )² - 32x²

= ( √2√x - 3 - 4√2x )( √2√x - 3 + 4√2x )

= ( √2x - 3 - 4√2x )( √2x - 3 + 4√2x )

c )

( x² + 2x  - 3 )² - ( x - 1 )² =

= ( x² + 2x - 3 - ( x - 1 ) )( x² + 2x - 3 + ( x - 1 ) )

= ( x² + 2x - 3 - x + 1 )( x² + 2x - 3 + x - 1 )

= ( x² + 2x - x - 2 )( x² + 4x - x - 4 )

= ( x ( x + 2 ) - ( x + 2 ) )( x ( x + 4 ) - ( x + 4 ) )

= ( x + 2 )( x - 1 )( x + 4 )( x - 1 )