Hello !
Ex.1 :
R=√(x+5)
1) si x=-5, R=√(-5+5)=√0=0
si x=-4, R=√(-4+5)=√1=1
si x=11, R=√(11+5)=√16=4
si x=29/4, R=√(29/4 + 5)=√(29/4 + 20/4)=√(49/4)=√49 / √4=7/2
2) si x=175, R=√(175+5)=√180=√(9*4*5)=√9*√4*√5=3*2*√5=6√5
3) Non
4) pour x < 0
Ex. 2 :
a) A = (3-7√5)(3+7√5)=3²-(7√5)²=9-245=-236
B = 2√15*7√3*4√5
= 56√225
= 56*15
= 840
b) C = √0,6*√480=√288=√144*√2=12√2
c) D = 7√3 - 3√75 + 2√48
= 7√3 - 3*√25*√3 + 2*√16*√3
= 7√3 - 3*5*√3 + 2*4*√3
= 7√3 - 15√3 + 8√3
= (7-15+8)*√3
= 0*√3
= 0
d) E = (7 - √3)² = 7² - 2*7*√3 + (√3)²
= 49- 14√3 + 3
= 52 - 14√3
Ex. 3 :
F = 27x² + 90x + 75 = 3(9x² + 30x + 25)
= 3(3x+5)²
G = (3x - 2)(2x + 5) + 12x - 8
= (3x - 2)(2x + 5) + 4(3x - 2)
= (3x - 2)[(2x + 5) + 4)]
= (3x -2) (2x +9)
H = 4x² + 28x + 49 + 3(2x+7)
= (2x+7)² + 3(2x+7)
= (2x+7)(2x+7) + 3(2x+7)
= (2x+7)[(2x+7)+3]
= (2x+7)(2x+10)
I = 16x² - 25 + (4x-5)(2x+3)
= (4x+5)(4x-5) + (4x-5)(2x+3)
= (4x-5)[(4x+5)+(2x+3)]
= (4x-5)(6x+8)
Ex. 4 :
[tex]J=2^4*2^5*4^2=2^4*2^5*2^2*2^2=2^{(4+5+2+2)}=2^{13}[/tex]
[tex]K=(5^3)^2*10^3=5^{3*2}*10^3=5^6*10^3[/tex]
