2 Math Qs 10PONITS!!!!!!

20. 2x^2-4x-k=0
let a, b are the roots of the equation such that a>b
ab = -k/2 (product of roots)
a+b = -(-4)/2 = 2 (sum of roots)
a-b = square of [(a-b)^2]
a-b = square of (a^2 - 2ab + b^2)
a-b = square of (a^2 + 2ab + b^2 - 4ab)
a-b = square of [(a+b)^2 - 4ab]
a-b = square of [(2)^2 - 4(-k/2)]
a-b = square of (4 + 2k)

22. consider triangle of ABD,
(sinα) / (sin∠ADB) = 2x / 3y (law of sines)-----(1)
consider triangle of BCD,
(sinβ) / (sin∠BDC) = x / 2y (law of sines)
(sinβ) / [sin(180degree - ∠ADB)] = x / 2y-----(2)
(sinβ) / sin∠ADB = x / 2y
(1)/(2): (sinα) / (sinβ) = (2x / 3y) / (x / 2y)
(sinα) / (sinβ) = (2x / 3y) * (2y / x)
(sinα) / (sinβ) = (4xy) / (3xy)
(sinα) / (sinβ) = 4/3