Question

√2x² - (2+√10)x+2√5=0

Answer 1

Ответ:

$\sqrt{2} {x}^{2} - (2 + \sqrt{10} )x + 2 \sqrt{5} = 0$

Дискриминант

$d = 4 + 4 \sqrt{10} + 10 - 8 \sqrt{10} = 14 - 4 \sqrt{10} = 1.35$

$x1 = \frac{2 + \sqrt{10} - \sqrt{1.35} }{2 \sqrt{2} } = 1.41$

$x2 = \frac{2 + \sqrt{10} + \sqrt{1.35} }{2 \sqrt{2} } = 2.24$

Answer 2

It seems like you have a quadratic equation that you'd like to solve for the variable "x". The given equation is:

√2x² - (2+√10)x + 2√5 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

In this equation, "a" is the coefficient of the quadratic term (x²), "b" is the coefficient of the linear term (x), and "c" is the constant term. Let's identify the coefficients from your equation:

a = √2 b = -(2+√10) c = 2√5

Now, plug these values into the quadratic formula and solve for "x":

x = (-(2+√10) ± √((2+√10)² - 4√2 * 2√5)) / (2√2)

Simplify the expression under the square root:

(2+√10)² - 4√2 * 2√5 = 4 + 4√10 + 10 - 16√10 = 14 - 12√10

Substitute this back into the formula:

x = (-(2+√10) ± √(14 - 12√10)) / (2√2)

Now you have two possible solutions for "x", each corresponding to the plus and minus signs in the formula:

x₁ = (-(2+√10) + √(14 - 12√10)) / (2√2) x₂ = (-(2+√10) - √(14 - 12√10)) / (2√2)

These are the exact solutions to the quadratic equation. If you need approximate numerical values, you can calculate them using a calculator.