if a =2x-1divided by 2x-2 and b =2-x divided by 2x-1 and a-b =0 find the value of X
Answers
Answer:
Step-by-step explanation:
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