Répondre :
A et B sous la forme a√5
A = 3√20 + 45 B =√180 + 3√5
A = 3√2²x5 + 45 B = √6²x5 + 3√5
A = 3x2√5 + 45 B = 6√5 + 3√5
A = 6√5 + 45 B = 9√5
A + B = 6√5 + 45 + 9√5 = 15√5 + 45
A x B = (6√5 + 45 )9√5 = 6√5 x 9√5 + 45 x 9√5 = 54 x√5² + 405√5
= 54 x 5 + 405√5 = 270 + 405√5 = 405√5 + 270
A/B = 6/√5 + 45 / 9/√5 = 6√5 /√5² + 9√5/√5² = 6√5/5 + 9√5/5 = 15√5/5
A = 3√20 + 45 B =√180 + 3√5
A = 3√2²x5 + 45 B = √6²x5 + 3√5
A = 3x2√5 + 45 B = 6√5 + 3√5
A = 6√5 + 45 B = 9√5
A + B = 6√5 + 45 + 9√5 = 15√5 + 45
A x B = (6√5 + 45 )9√5 = 6√5 x 9√5 + 45 x 9√5 = 54 x√5² + 405√5
= 54 x 5 + 405√5 = 270 + 405√5 = 405√5 + 270
A/B = 6/√5 + 45 / 9/√5 = 6√5 /√5² + 9√5/√5² = 6√5/5 + 9√5/5 = 15√5/5
Bonjour,
Exercice 1
A = 3(x-6) = 3x -18
B = (5x+1)(2x-7)
=(5x)*(2x) +(5x)*(-7) + (1)*(2x) + (1)*(-7)
= 10x² -35x +2x -7
= 10x² -33x -7
C = (x+2)² = (x² +2*x*2 +2²) = x² +4x+4
D = (10x-1)(12x+1)
=(10x)*(12x) +(10x)*(1) + (-1)*(12x) + (-1)*(1)
= 120x² +10x -12x -1
= 120x² -2x -1
Exercice 2
E = 6x+18 = 6(x+3)
F = (3x+4)² + (3x+4)(x-8)
= (3x+4)(3x+4) + (3x+4)(x-8)
= (3x+4)((3x+4) +(x-8))
= (3x+4)(3x+4 +x-8)
= (3x+4)(4x-4)
= 4(3x+4)(x-1)
Exercice 3
Avec la calculatrice :
A = √200 = 14,14
B = √141 +3 = 11,88 + 3 = 14,88
C = (5-√11)/(13√15 +1) = (5-3,32)/(50,35+1) = 1,68/51,35 = 0,03
Exercice 4
1-
A = 3√20 +4√5 = 3√(4*5) + 4√5
= 3*√4*√5 +4√5 = 3*2*√5 +4√5
= 6√5 +4√5 = 10√5
B = √180 +3√5 = √(36*5) +3√5
= √36*√5 +3√5 =6√5 + 3√5
= 9√5
2-
A + B = 10√5 + 9√5 = 19√5
3-
A×B = 10√5×9√5 = 90×√5² = 90×5 = 450
4-
A/B = 10√5/9√5 = 10/9
Exercice 1
A = 3(x-6) = 3x -18
B = (5x+1)(2x-7)
=(5x)*(2x) +(5x)*(-7) + (1)*(2x) + (1)*(-7)
= 10x² -35x +2x -7
= 10x² -33x -7
C = (x+2)² = (x² +2*x*2 +2²) = x² +4x+4
D = (10x-1)(12x+1)
=(10x)*(12x) +(10x)*(1) + (-1)*(12x) + (-1)*(1)
= 120x² +10x -12x -1
= 120x² -2x -1
Exercice 2
E = 6x+18 = 6(x+3)
F = (3x+4)² + (3x+4)(x-8)
= (3x+4)(3x+4) + (3x+4)(x-8)
= (3x+4)((3x+4) +(x-8))
= (3x+4)(3x+4 +x-8)
= (3x+4)(4x-4)
= 4(3x+4)(x-1)
Exercice 3
Avec la calculatrice :
A = √200 = 14,14
B = √141 +3 = 11,88 + 3 = 14,88
C = (5-√11)/(13√15 +1) = (5-3,32)/(50,35+1) = 1,68/51,35 = 0,03
Exercice 4
1-
A = 3√20 +4√5 = 3√(4*5) + 4√5
= 3*√4*√5 +4√5 = 3*2*√5 +4√5
= 6√5 +4√5 = 10√5
B = √180 +3√5 = √(36*5) +3√5
= √36*√5 +3√5 =6√5 + 3√5
= 9√5
2-
A + B = 10√5 + 9√5 = 19√5
3-
A×B = 10√5×9√5 = 90×√5² = 90×5 = 450
4-
A/B = 10√5/9√5 = 10/9
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