1) x² -7x + 5 = (2x + 1)²
x² - 7x + 5 = 4x² + 4x + 1
3x² +11x - 4 = 0
D = b² - 4ac = 11² - 4*3*(-4) = 121 + 48 = 169
√D = √169 = 13
x1 = (-b + √D)/2a = (-11+13)/2*3 = 1/3
x2 = (-b - √√D)/2a = (-11 - 13)/2*3 = -4
2) 6x²+x+7=(1-3x)²
6x²+x+7=1 - 6x + 9x²
3x² -7x -6 = 0
D = b² - 4ac = 49 + 4*3*6 = 49 + 72 = 121
√D = √121 = 11
x1 = (7+11)/2*6 = 1,5
x2 = (7-11)/2*6 = - 1/3
3) 2x² + 5x -3 = (x + 1)²
2x² + 5x -3 =x² + 2x + 1
x² + 3x - 4 = 0
По т.Виета
x1 + x2 = -3 x1 = -4
x1 * x2 = -4 x2 = 1
4) 3x² - 4x + 2 = (x + 4)²
3x² - 4x + 2 =x² + 8x + 16
2x² -12x -14 = 0
x² - 6x - 7 = 0
По т.Виета
x1 + x2 = 6 x1 = 7
x1 * x2 = -7 x2 = - 1
1) x + 11 = (1 + √x)²
x + 11 = 1 + 2√x + x
2√x = 10
√x = 5
x = 5²
x = 25
2) x + 19 = (1 + √x)²
x + 19 = 1 + 2√x + x
2√x = 18
√x = 9
X = 81