Question

In the given figure find the value of x.
Pls give the correct answer to get brainliest

Answer 1

As DE || BC ,

AD/BD = AE/EC

or, (4x-3)/(3x-1)=(8x-7)/(5x-3) [ putting the values ]

or, (4x-3)(5x-3)=(8x-7)(3x-1)

or, 20x^2-12x-15x+9 = 24x^2-8x-21x+21

or, 20x^2 -27x +9 = 24x^2-29x+7

or, 20x^2 -24x^2 -27x +29x = 7 -9

or, -4x^2 +2x = -2

or, -2 = -4x^2 + 2x

or, 4x^2 - 2x -2 =0

or, 4x^2-4x+2x-2=0

or, 4x(x-1)+2(x-1)=0

or, (4x+2)(x-1)=0

or, 2(2x+1)(x-1)=0

or, (2x+1)(x-1)=0

Therefore,

Either,2x+1 =0 or x-1 =0

If ,it is considered 2x+1 =0 , the value of x will be

2x+1=0

or, 2x =-1

or, x = -½

And it is not applicable ,means a length of a triangle can't be negetive.So, x ≠ - ½

Now, the only equation left is x-1 =0

or, x=1

Therefore, the answer is 1.