Area = base × height
Given that the area is 1m² and the base is (2x-1) meters and the height is (4x-7) meters, we have:
1 = (2x-1) × (4x-7)
Expanding the expression:
1 = 8x^2 - 14x - 4x + 7
1 = 8x^2 - 18x + 7
Now, let's bring 1 to the left side:
0 = 8x^2 - 18x + 7 - 1
0 = 8x^2 - 18x + 6
Now, let's simplify the equation by dividing all terms by 2:
0 = 4x^2 - 9x + 3
So, we have shown that 4x^2 - 9x + 3 = 0.
