Ch02 31

Ch02 31

• 1.
  Exercice 31 3 (a) 3 x 3 x = x 1/3 x 1/3 = x 2/3 = x2 (b) 2 2+ 3 = ( 2)2 + 2 2 3 + ( 3)2 =2+2 6+3=5+2 6
• 2.
  Exercice 31 (suite..) (c) α+ β α− β (α + β)2 + (α − β)2 + = α− β α+ β α2 − ( β)2 α2 + 2α β+( β)2 + α2 − 2α β+( β)2 = α2 − β α2 + 2α β + β + α2 − 2α β+β = α2 − β 2α2 + 2β = α2 − β 2(α2 + β) = 2 α −β
• 3.
  Exercice 31 (suite..) (d) 2+ 2 1+ 2 1+ + 1+ 2 1− 2 (1 + 2)(1 − 2) (2 + 2)(1 − 2) (1 + 2)(1 + 2) = + + (1 + 2)(1 − 2) (1 + 2)(1 − 2) (1 + 2)(1 − 2) 1−2 − 2 3+2 2 = 2−2 + 2 + 2 1 1 −2 1 −2 −1 − 2 + 3 + 2 2 = −1 2+ 2 = −1 = −2 − 2
• 4.
  Exercice 31 (suite..) (e) x3 + x2 y + xy2 + y3 = x 2 (x + y) + y2 (x + y) =x x+y+y x+y = (x + y) x+y (f) x+y x−y x+y x−y − = − x−y x+y x−y x+y x+y x+y− x−y x−y = x−y x+y (x + y) − (x − y) 2y = = (x − y)(x + y) x 2 − y2
• 5.
  Exercice 31 (suite..) (g) 1 x− y = x+ y ( x + y)( x − y) x− y x− y = = ( x)2 − ( y)2 x−y (h) h−4 h−4 h−4 = h+4 h+4 h−4 ( h − 4)2 ( h − 4)2 = = ( h)2 − 42 h − 16
• 6.
  Exercice 31 (suite..) (i) 16x 2 − y2 16x 2 − y2 2 x + y = 2 x− y 2 x− y2 x+ y (16x 2 − y2 )(2 x + y) = 4x − y (4x − y)(4x + y)(2 x + y) = 4x − y = (4x + y)(2 x + y) (j) 1 1 ∆− ∆−2 = ∆+ ∆−2 ∆+ ∆−2 ∆− ∆−2 ∆− ∆−2 ∆− ∆−2 = = ∆ − (∆ − 2) 2