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

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

Answer 2

(a-b)^2 = (a+b)^2 - 4ab = 25 - 4*(-2) = 25 + 8 = 33