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We know that,
Diagonals of a parallelogram bisect each other.
So,
AO/ CO = BO/ DO
⇒ 4/ (4x – 2) = (x +1)/ (2x + 4)
4(2x + 4) = (4x – 2)(x +1)
8x + 16 = x(4x – 2) + 1(4x – 2)
8x + 16 = 4x
2
– 2x + 4x – 2
-4x
2
+ 8x + 16 + 2 – 2x = 0
-4x
2
+ 6x + 8 = 0
4x
2
– 6x – 18 = 0
4x
2
– 12x + 6x – 18 = 0
4x(x – 3) + 6(x – 3) = 0
(4x + 6) (x – 3) = 0
∴
x = – 6/4 or x = 3
We know that,
Diagonals of a parallelogram bisect each other
So,
AO/ CO = BO/ DO
⇒ (6x – 5)/ (2x + 1) = (5x – 3)/ (3x – 1)
(6x – 5)(3x – 1) = (2x + 1)(5x – 3)
3x(6x – 5) – 1(6x – 5) = 2x(5x – 3) + 1(5x – 3)
18x
2
– 10x
2
– 21x + 5 + x +3 = 0
8x
2
– 16x – 4x + 8 = 0
8x(x – 2) – 4(x – 2) = 0
(8x – 4)(x – 2) = 0
x = 4/8 = 1/2 or x = -2
∴
x= 1/2
We know that,
Diagonals of a parallelogram bisect each other
So,
AO/ CO = BO/ DO
(3x – 19)/ (x – 3) = (x–4)/ 4
4(3x – 19) = (x – 3) (x – 4)
12x – 76 = x(x – 4) -3(x – 4)
12x – 76 = x
2
– 4x – 3x + 12
-x
2
+ 7x – 12 + 12x -76 = 0
-x
2
+ 19x – 88 = 0
x
2
– 19x + 88 = 0
x
2
– 11x – 8x + 88 = 0
x(x – 11) – 8(x – 11) = 0
∴
x = 11 or x = 8
