Sagot :
Réponse :
Explications étape par étape
Bonsoir,
Résoudre les équations suivantes :
5x² +14x-3 =0
(x√5)² + 2 * x√5 * 7/√5 + (7/√5)² - (7/√5)² - 3 = 0
(x√5 + 7/√5)² - 49/5 - 15/5 = 0
(x√5 + 7/√5)² - 64/5 = 0
(x√5 + 7/√5 - 8/√5)(x√5 + 7/√5 + 8/√5) = 0
(x√5 - 1/√5)(x√5 + 15/√5) = 0
x√5 - 1/√5 = 0 ou x√5 + 15/√5 = 0
x√5 = 1/√5 ou x√5 = -15/√5
x = 1/(√5)² ou x = -15/(√5)²
x = 1/5 ou x = -15/5
x = 1/5 ou x = -3
X² -29x+210=0
x² - 2 * x * 29 + 29² - 29² + 210 = 0
(x - 29)² - 841 + 210 = 0
(x - 29)² - 631 = 0
(x - 29 - √631)(x - 29 + √631) = 0
x - 29 - √631 = 0 ou x - 29 + √631
x = 29 + √631 ou x = 29 - √631
X²-x+1÷4=0
x² - 2 * x * 1/2 + (1/2)² = 0
(x - 1/2)² = 0
x - 1/2 = 0
x = 1/2
4x²+3x+1=0
(2x)² + 2 * 2x * 3/4 + (3/4)² - (3/4)² + 1 = 0
(2x + 3/4)² - 9/16 + 16/16 = 0
(2x + 3/4)² + 7/16 = 0
(2x + 3/4)² = -7/6 < 0 un carré n'est jamais négatif donc pas de solution
X²+x-2=0
x² + 2 * x * 1/2 + (1/2)² - (1/2)² - 2 = 0
(x + 1/2)² - 1/4 - 8/4 = 0
(x + 1/2)² - 9/4 = 0
(x + 1/2 - 3/2)(x + 1/2 + 3/2) = 0
(x - 2/2)(x + 4/2) = 0
(x - 1)(x + 2) = 0
x - 1 = 0 ou x + 2 = 0
x = 1 ou x = -2
7x²-5x-2=0
(x√7)² - 2 * x√7 * 5/(2√7) + [5/(2√7)]² - [5/(2√7)]² - 2 = 0
[x√7 - 5/(2√7)]² - 25/(4 * 7) - 2 = 0
[x√7 - 5/(2√7)]² - 25/28 - 56/28 = 0
[x√7 - 5/(2√7)]² - 81/28 = 0
[x√7 - 5/(2√7) - 9/(2√7)][x√7 - 5/(2√7) + 9/(2√7)] = 0
[x√7 - 14/(2√7)][x√7 + 4/(2√7)] = 0
(x√7 - 7/√7)(x√7 + 2/√7) = 0
x√7 - 7/√7 = 0 ou x√7 + 7/√7 = 0
x√7 = 7/√7 ou x√7 = -7/√7
x = 7/7 ou x = -7/7
x = 1 ou x = -1
2x²+2x-4=0
2(x² + x - 2) = 0
x² + x - 2 = 0
x² + 2 * x * 1/2 + (1/2)² - (1/2)² - 2 = 0
(x + 1/2)² - 1/4 - 8/4 = 0
(x + 1/2)² - 9/4 = 0
(x + 1/2 - 3/2)(x + 1/2 + 3/2) = 0
(x - 2/2)(x + 4/2) = 0
(x - 1)(x + 2) = 0
x - 1 = 0 ou x + 2 = 0
x = 1 ou x = -2
0,2x²-1,7x+0,5=0
2x² - 17x + 5 = 0
(x√2)² - 2 * x√2 * 17/(2√2) + [17/(2√2)]² - [17/(2√2)]² + 5 = 0
[x√2 - 17/(2√2)]² - 289/8 + 40/8 = 0
[x√2 - 17/(2√2)]² - 249/8 = 0
[x√2 - 17/(2√2) - √249/(2√2)][x√2 - 17/(2√2) + √249/(2√2)] = 0
x√2 - 17/(2√2) - √249/(2√2) = 0 ou x√2 - 17/(2√2) + √249/(2√2) = 0
x√2 = 17/(2√2) + √249/(2√2) ou x√2 = 17/(2√2) - √249/(2√2)
x = 17/4 + √249/4 ou x = 17/4 - √249/4
7x²-6x-1=0
(x√7)² - 2 * x√7 * 3/√7 + (3/√7)² - (3/√7)² - 1 = 0
(x√7 - 3/√7)² - 9/7 - 7/7 = 0
(x√7 - 3/√7)² - 16/7 = 0
(x√7 - 3/√7 - 4/√7)(x√7 - 3/√7 + 4/√7) = 0
(x√7 - 7/√7)(x√7 + 1/√7) = 0
x√7 - 7/√7 = 0 ou x√7 + 7/√7 = 0
x√7 = 7/√7 ou x√7 = -7/√7
x = 7/7 ou x = -7/7
x = 1 ou x = -1
3x²-7x+2=0
(x√3)² - 2 * x√3 * 7/(2√3) + [7/(2√3)]² - [7/(2√3)]² + 2 = 0
[x√3 - 7/(2√3)]² - 49/12 + 24/12 = 0
[x√3 - 7/(2√3)]² - 25/12 = 0
[x√3 - 7/(2√3) - 5/(2√3)][x√3 - 7/(2√3) + 5/(2√3)] = 0
[x√3 - 12/(2√3)][x√3 - 2/(2√3)] = 0
(x√3 - 6/√3)(x√3 - 1/√3) = 0
x√3 - 6/√3 = 0 ou x√3 - 1/√3 = 0
x√3 = 6/√3 ou x√3 = 1/√3
x = 6/3 ou x = 1/3
x = 2 ou x = 1/3
Je pense que tu as compris je te laisse faire les dernières.
4x²+3x-1=0
3x²+4x+1=0
3x²+x-4=0
X²+5x-24=0
