Question

а+в=5, ав= -2. Найти значение (а-в)²

Answer 1

$left { {{a+b=5} atop {ab=-2}} right. ; = textgreater left { {{a=5-b} atop {a=-2:b}}. right$

5 - b = - 2 : b
5b - b² = - 2
b² - 5b - 2 = 0
D = - 5² - 4 * (- 2) = 25 + 8 = 33
$b_{1} = frac{5+ sqrt{33} }{2} \ \ b_{2} = frac{5- sqrt{33} }{2}$

a = 5 - b
$a_{1} =5- frac{5+ sqrt{33} }{2} \ \ a _{2} =5- frac{5- sqrt{33} }{2}$

$(a-b) ^{2} =(5- frac{5+ sqrt{33} }{2} - frac{5+ sqrt{33} }{2} ) ^{2} =(5- frac{5}{2} - frac{ sqrt{33} }{2} - frac{5}{2} - frac{ sqrt{33} }{2} ) ^{2} = \ \ =(5- frac{10}{2} - frac{2 sqrt{33} }{2} ) ^{2} =(- sqrt{33} ) ^{2} =33$