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Question
In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC
If AD = 8x − 7, DB = 5x − 3, AE = 4x − 3 and EC = (3x − 1), find the value of x.
Solution
We have,
DE || BC
Therefore, by basic proportionality theorem, we have,
`"AD"/"DB"="AE"/"EC"`
`rArr(8x-7)/(5x-3)=(4x-3)/(3x-1)`
⇒ (8x − 7)(3x − 1) = (4x − 3)(5x − 3)
⇒ 24x2 − 8x − 21x + 7 = 20x2 − 12x − 15x + 9
⇒ 24x2 − 20x2 − 29x + 27x + 7 − 9 = 0
⇒ 4x2 − 2x − 2 = 0
⇒ 2[2x2 − x − 1] = 0
⇒ 2x2 − x − 1 = 0
⇒ 2x2 − 2x + 1x − 1 = 0
⇒ 2x(x − 1) + 1(x − 1) = 0
⇒ (2x + 1) (x – 1) = 0
⇒ 2x + 1 = 0 or x – 1 = 0
⇒ x = −1/2 or x = 1
𝑥 = −1/2 is not possible
∴ x = 1
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