Question

(2x-5)²-1=0
Can you solve this?

Answer 1

(2x-5)²-1=0

Using

$a {}^{2} - b {}^{2} = (a + b)(a - b)$

$(2x - 5 - 1)(2x - 5 + 1) = 0 \\ \\ (2x - 6)(2x - 4) = 0 \\ \\ 2(x - 3) \times 2(x - 2) = 0 \\ \\ x - 3 = 0 \\ \\ x - 2 = 0 \\ \\ x = 3 \\ \\ x = 2$

x1 = 3 and X2 = 2

Answer 2

$\huge\underline\mathbb\color{red}{Answer}$

${(2x - 5)}^{2} - 1 = 0$

Use the identity (a+b)²=a²+b²+2ab

${(2x)}^{2} + {5}^{2} - 2(2x)(5) - 1 = 0$

${4x}^{2} + 25 - 20x - 1 = 0$

${4x}^{2} - 20 x + 24 = 0$

Simplify by reducing it by 4

${x}^{2} - 5x + 6 = 0$

${x}^{2} - 2x - 3x + 6 = 0$

$x(x - 2) - 3(x - 2) = 0$

$(x - 2) = 0 \: \: \: \: \: \: \: \: \: (x - 3 )= 0$

$x = 2 \: \: \: \: \: \: \: \: \: \: x = 3$