Question

solve by factorization

Answer 1

$<b >Hey here is your answer$

$= {2x}^{2} - 2x + \frac{1}{2} = 0$
multiply both sides by 2 :-

$= 2( {2x}^{2} - 2x + \frac{1}{2} ) = 2 \times 0 \\ \\ = 4 {x}^{2} - 4x + 1 = 0 \\ \\ = {4x}^{2} - 2x - 2x + 1 = 0 \\ \\ = 2x(2x - 1) - 1(2x - 1) = 0 \\ \\ \bf = (2x - 1)(2x - 1) = 0 \\ \\ = {(2x - 1)}^{2} = 0 \\ \\ = 2x - 1 = \sqrt{0} \\ \\ = 2x - 1 = 0 \\ \\ = 2x = 1 \\ \\ \bf = x = \frac{1}{2} \: \: \: answer \:$

hope this helps you

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Answer 2

Hi ,

Given Quadratic equation

2x² - 2x + 1/2 = 0

=>(√2x)² -2×(√2x)×(1/√2)+(1/√2)²=0

=> ( √2x - 1/√2 )² = 0

[ a² - 2ab + b² = ( a - b )² ]

=> (√2x-1/√2)(√2x-1/√2)=0

Therefore ,

(√2x-1/√2)= 0 or (√2x -1/√2)=0

√2x = 1/√2 or √2x = 1/√2

x = 1/2 or x = 1/2

Equal roots.

I hope this helps you.

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