Question

(x ^ 2)/2 - 2 1/2 * x - 7 = 0​

Answer 1

$\displaystyle\bf\\\frac{x^{2} }{2} -2\frac{1}{2} x-7=0\\\\\\\frac{x^{2} }{2} \cdot 2-\frac{5}{2} x\cdot 2-7\cdot 2=0\\\\\\x^{2} -5x-14=0\\\\D=(-5)^{2}-4\cdot(-14)=25+56=81=9^{2} \\\\\\x_{1} =\frac{5-9}{2} =\frac{-4}{2} =-2\\\\\\x_{2} =\frac{5+9}{2} =\frac{14}{2} =7\\\\\\Otvet \ : \ -2 \ \ ; \ \ 7$

Answer 2

To solve the quadratic equation (x^2)/2 - (2^(1/2)) * x - 7 = 0, you can use the quadratic formula, which is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In your equation, a = 1/2, b = -2^(1/2), and c = -7. Now, plug these values into the quadratic formula:

x = (-(-2^(1/2)) ± √((-2^(1/2))^2 - 4(1/2)(-7))) / (2(1/2))

Simplify further:

x = (2^(1/2) ± √(2 - 4(1/2)(-7))) / (2(1/2))

x = (2^(1/2) ± √(2 + 14)) / (2(1/2))

x = (2^(1/2) ± √16) / (2(1/2))

x = (2^(1/2) ± 4) / (2(1/2))

Now, you can simplify the expression further by factoring out 2^(1/2) from the numerator:

x = (2^(1/2)(1 ± 2)) / (2(1/2))

The square root and the 2^(1/2) in the numerator and denominator cancel out:

x = (1 ± 2)

So, you have two solutions:

1. x = 1 + 2 = 3
2. x = 1 - 2 = -1

Therefore, the solutions to the equation (x^2)/2 - (2^(1/2)) * x - 7 = 0 are x = 3 and x = -1.