Question

4х² - 8х - 85 = 0, t = 3 Найти t*x1*x2 ÷ x1 + x2

Answer 1

4х² - 8х - 85 = 0, t = 3

х₁+х₂=8:4=2

х₁*х₂=85:4=-21,25

3*(-21,25)/2=-63,75:2=-31,875

Answer 2

4x² - 8x - 85 = 0

По теореме Виета:

x1 + x2 = - b/a = -(-8)/4 = 2

x1*x2 = c/a = -85/4

3*(-85/4) : 2 = -255/8

Answer 3

To solve the quadratic equation 4x² - 8x - 85 = 0 and find the value of t * x1 * x2 ÷ (x1 + x2) when t = 3, we first need to find the roots (x1 and x2) of the equation.

The quadratic equation is of the form ax² + bx + c = 0, where: a = 4 b = -8 c = -85

To find the roots, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a

Let's calculate the roots (x1 and x2):

1. Calculate the discriminant (D): D = b² - 4ac D = (-8)² - 4 * 4 * (-85) D = 64 + 1360 D = 1424

2. Calculate the roots (x1 and x2): x1 = (-(-8) + √1424) / (2 * 4) x1 = (8 + √1424) / 8

x2 = (-(-8) - √1424) / (2 * 4) x2 = (8 - √1424) / 8

Now, let's find the value of t * x1 * x2 ÷ (x1 + x2) when t = 3:

t = 3 x1 = (8 + √1424) / 8 x2 = (8 - √1424) / 8

t * x1 * x2 ÷ (x1 + x2) = 3 * [(8 + √1424) / 8] * [(8 - √1424) / 8] ÷ [((8 + √1424) / 8) + ((8 - √1424) / 8)]

Now, let's simplify the expression:

t * x1 * x2 ÷ (x1 + x2) = 3 * [(8 + √1424)(8 - √1424)] ÷ [8(8 + √1424) + 8(8 - √1424)] t * x1 * x2 ÷ (x1 + x2) = 3 * (64 - 1424) ÷ (64 + 64) t * x1 * x2 ÷ (x1 + x2) = 3 * (-1360) ÷ 128 t * x1 * x2 ÷ (x1 + x2) = -4080 ÷ 128 t * x1 * x2 ÷ (x1 + x2) = -31.875

So, when t = 3, the value of t * x1 * x2 ÷ (x1 + x2) is -31.875.