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In below figure, If AB || CD, find the value of x.
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Since diagonals of a trapezium divide each other proportionally.
`therefore"AO"/"OC"="BO"/"OD"`
`rArr4/(4x-2)=(x+1)/(2x+4)`
⇒ 4(2ЁЭСе + 4) = (ЁЭСе + 1)(4ЁЭСе − 2)
⇒ 8x + 16 = x(4x – 2) +1(4x – 2)
⇒ 8x + 16 = 4x2 + 2x – 2
⇒ 4x2 + 2ЁЭСе − 8ЁЭСе − 2 − 16 = 0
⇒ 4x2 − 6ЁЭСе − 18 = 0
⇒ 2[2ЁЭСе2 − 3ЁЭСе − 9] = 0
⇒ 2ЁЭСе2 − 3ЁЭСе − 9 = 0
⇒ 2ЁЭСе(ЁЭСе − 3) + 3(ЁЭСе − 3) = 0
⇒ (ЁЭСе − 3)(2ЁЭСе + 3) = 0
⇒ ЁЭСе − 3 = 0 or 2ЁЭСе + 3 = 0
⇒ ЁЭСе = 3 or ЁЭСе = -3/2
ЁЭСе = -3/2 is not possible, because
`"OB"=x+1=-3/2+1=-1/2`
Length cannot be negative
`therefore"AO"/"OC"="BO"/"OD"`
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