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In the below figure, If AB || CD, find the value of x.
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`rArr(3x-1)/(5x-3)=(2x+1)/(6x-5)`
⇒ (3x – 1) (6x – 5) = (2x + 1) (5x – 3)
⇒ 3x (6x – 5) – 1(6x – 5) = 2x (5x – 3) + 1 (5x – 3)
⇒ 18ЁЭСе2 − 15ЁЭСе − 6ЁЭСе + 5 = 10ЁЭСе2 − 6ЁЭСе + 5ЁЭСе − 3
⇒ 8ЁЭСе2 − 20ЁЭСе + 8 = 0
⇒ 4(2ЁЭСе2 − 5ЁЭСе + 2) = 0
⇒ 2ЁЭСе2 − 4ЁЭСе − 1ЁЭСе + 2 = 0
⇒ 2ЁЭСе(ЁЭСе − 2) − 1(ЁЭСе − 2) = 0
⇒ (2ЁЭСе − 1)(ЁЭСе − 2) = 0
⇒ 2x – 1 = 0 or x – 2 = 0
⇒ ЁЭСе = 1/2 or ЁЭСе = 2
ЁЭСе = 1/2 is not possible, because, OC = 5x – 3
`= 5(1/2) - 3`
`=(5-6)/2=-1/2`
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