Question

if a = 2 x-1/2x-2 b = 2-x/2 x+1 and a-b=0 find the value of x.

Answer 1

Answer:

$Value \: of \: x = \frac{1±i}{2}$

Step-by-step explanation:

$Given \: a = \frac{2x-1}{2x-2},\\b=\frac{2-x}{2x+1}$

$and \\ a-b=0$

$\implies \frac{2x-1}{2x-2} - \frac{2-x}{2x+1}=0$

$\implies \frac{(2x-1)(2x+1)-(2-x)(2x-2)}{(2x-2)(2x+1)}=0$

$\implies \frac{(2x)^{2}-1^{2}-(4x-4-2x^{2}+2x}{(2x-2)(2x+1)}=0$

$\implies 4x^{2}-1-4x+4+2x^{2}-2x=0$

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

$\implies 3(2x^{2}-2x+1)=0$

$\implies 2x^{2}-2x+1=0$

Compare above equation with ax²+bx+c=0 ,we get

$a = 2 , b = -2 , c = 1$

$Discreminant (D) = b^{2}-4ac$

$= (-2)^{2}-4\times 2 \times 1\\=4-8\\=-4$

/* By quadratic formula :

$x = \frac{-b±\sqrt{D}}{2a}$

$= \frac{-(-2)±\sqrt{-4}}{2\times 2}$

$= \frac{2±2i}{4}\\=\frac{2(1+i)}{4}\\=\frac{1±i}{2}$

Therefore.,

$Value \: of \: x = \frac{1±i}{2}$

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Answer 2

Answer:

Answer:

Value \: of \: x = \frac{1±i}{2}Valueofx=

2

1±i

Step-by-step explanation:

\begin{lgathered}Given \: a = \frac{2x-1}{2x-2},\\b=\frac{2-x}{2x+1}\end{lgathered}

Givena=

2x−2

2x−1

,

b=

2x+1

2−x

\begin{lgathered}and \\ a-b=0\end{lgathered}

and

a−b=0

\implies \frac{2x-1}{2x-2} - \frac{2-x}{2x+1}=0⟹

2x−2

2x−1

−

2x+1

2−x

=0

\implies \frac{(2x-1)(2x+1)-(2-x)(2x-2)}{(2x-2)(2x+1)}=0⟹

(2x−2)(2x+1)

(2x−1)(2x+1)−(2−x)(2x−2)

=0

\implies \frac{(2x)^{2}-1^{2}-(4x-4-2x^{2}+2x}{(2x-2)(2x+1)}=0⟹

(2x−2)(2x+1)

(2x)

2

−1

2

−(4x−4−2x

2

+2x

=0

\implies 4x^{2}-1-4x+4+2x^{2}-2x=0⟹4x

2

−1−4x+4+2x

2

−2x=0

\implies 6x^{2}-6x+3=0⟹6x

2

−6x+3=0

\implies 3(2x^{2}-2x+1)=0⟹3(2x

2

−2x+1)=0

\implies 2x^{2}-2x+1=0⟹2x

2

−2x+1=0

Compare above equation with ax²+bx+c=0 ,we get

a = 2 , b = -2 , c = 1a=2,b=−2,c=1

Discreminant (D) = b^{2}-4acDiscreminant(D)=b

2

−4ac

\begin{lgathered}= (-2)^{2}-4\times 2 \times 1\\=4-8\\=-4\end{lgathered}

=(−2)

2

−4×2×1

=4−8

=−4

/* By quadratic formula :

x = \frac{-b±\sqrt{D}}{2a}x=

2a

−b±

D

= \frac{-(-2)±\sqrt{-4}}{2\times 2}=

2×2

−(−2)±

−4

\begin{lgathered}= \frac{2±2i}{4}\\=\frac{2(1+i)}{4}\\=\frac{1±i}{2}\end{lgathered}

=

4

2±2i

=

4

2(1+i)

=

2

1±i

Therefore.,

Value \: of \: x = \frac{1±i}{2}Valueofx=

2

1±i