Question

ДАЮ 98 БАЛОВ!!
1) y²+12y-6=0
2) y²-5y-10=0
3) 2x²+4x+5/6=0

Answer 1

1)
${y}^{2} + 12y - 6 = 0 \\ d = {b}^{2} - 4ac = 144 + 24 = 168 = {2 \sqrt{42} }^{2} \\ y = \frac{ - 12 + 2 \sqrt{42} }{2} = - 6 + \sqrt{42} \\ y = \frac{ - 12 + 2 \sqrt{42} }{2} = - 6 - \sqrt{42}$
2)
${y}^{2} - 5y - 10 = 0 \\ d = 25 + 40 = 65 = { \sqrt{65} }^{2} \\ y = \frac{5 + \sqrt{65} }{2} \\ y = \frac{5 - \sqrt{65} }{2}$
3)
$2 {x}^{2} + 4x + \frac{5}{6} = 0 \\ d = 16 - 6 \frac{2}{3} =9 \frac{1}{3} = { \sqrt{9 \frac{1}{3} } }^{2} \\ y = \frac{ - 4 - 9 \frac{1}{3} }{4} \\ y = \frac{ - 4 + 9 \frac{1}{3} }{4}$

Answer 2

1)
y^2 + 12y - 6 = 0
y = -6 +- √(36 + 6) = -6 +- √(42)

2)
y^2 - 5y - 10 = 0
y = 1/2 (5 +- √(25 + 40) ) = 1/2 (5 +- √(65))

3)
2x^2 + 4x + 5/6 = 0
x = 1/2 (-2 +- √(4 - 10/6) ) = -1 +- √(1 - 5/12) = -1 +- √(7/12)