Explications étape par étape:
bsr
ex 8
1) 64 - 25x^2
8^2 - 5^2 x^2
8^2 - (5X)^2
(8 - 5X) ( 8 + 5X)
2) 64 - 25x^2 - ( 8X + 3)( 8 - 5X)
(8 - 5X) ( 8 + 5X) - ( 8X + 3)( 8 - 5X)
(8 - 5X ) (8 + 5X - 8X - 3)
(8 - 5X) ( - 3X + 5)
ex9
1)
49X^2 - 28X +4 - 25
(7X - 2)^2 - 5^2
(7X -2 - 5)(7X -2 +5)
(7X -7)(7X +3)
2)
( X + 5)^2 - 121
( X + 5)^2 - 11^2
( X + 5 - 11 ) ( X + 5 + 11)
(X - 6 ) ( X + 16 )
ex 10
1ere figure on a la décompose en 2 rectangles
aire 1ere rectangle = 5X
aire du 2nd rectangle = (5 + X)X
= 5X + X^2
aire 1 + aire 2 = 5X + 5X + X^2
aire totale = 10X + X^2
aire d'un triangle = ( H×B)/2
= [ 2X × (10 + X) ] /2
= (20X + 2X^2 ) /2
= 2 ( 10X + X^2) / 2
= 10X + X^2
donc les deux figures ont mes mêmes aires
ex 11
A= 9 - ( 2X - 3)^2
A = 3^2 - ( 2X - 3)^2
A = (3 - 2X + 3 ) ( 3 + 2X - 3)
A = ( -2X + 6)( 2X )
A = 2( -X + 3)(2X)
B = (3X - 7)^2 - 49
B = ( 3X - 7)^2 - 7^2
B = ( 3X - 7 - 7) ( 3X - 7 +7)
B = ( 3X - 14)( 3X)
A+B = 9 - ( 2X - 3)^2 + (3X - 7)^2 - 49
A+B = 9 - 49 + (3X - 7)^2 - ( 2X - 3)^2
A+B = -40 +(3X-7-2X+3)( 3X -7+2X -3)
A+B = - 40 + (X- 4)(5X - 10)
A+B = - 40 + 5 ( X-4)(X -2)
A+B = 5 [ -8 + ( X-4)(X -2)]
A+B = 5 [-8 + ( -4)(-2)] pour X = 0
A+B = 5 (0)
A+B = 0
A+B = 5 [ -8 + ( 2)(4)]
A+B = 5 ( 0)
A+B = 0