Ques no 28 ....
please fast.
Its till ; only
Answers
Answer:
x = \frac{6}{5}\:Or \:x = -5
Step-by-step explanation:
Given \: \frac{x+1}{x-2}+\frac{x-2}{x+2}\\=4-\frac{2x+3}{x-2}
\implies \frac{x-2}{x+2}+\frac{2x+3}{x-2}\\=4-\frac{x+1}{x-1}
\implies \frac{(x-2)^{2}+(x+2)(2x+3)}{(x+2)(x-2)}\\=\frac{4(x-1)-(x+1)}{x-1}
\implies \frac{x^{2}-4x+4+2x^{2}+3x+4x+6}{x^{2}-2^{2}}\\=\frac{4x-4-x-1}{x-1}
\implies \frac{3x^{2}+3x+10}{x^{2}-4}\\=\frac{3x-5}{x-1}
\implies (x-1)(3x^{2}+3x+10)\\=(x^{2}-4)(3x-5)
\implies (3x^{3}+3x^{2}+10x-3x^{2}-3x-10)\\=(3x^{3}-5x^{2}-12x+20)
\implies (3x^{3}+7x-10)-(3x^{3}-5x^{2}-12x+20)=0
\implies (3x^{3}+7x-10-3x^{3}+5x^{2}+12x-20)=0
\implies 5x^{2}+19x-30=0
Compare above equation with
ax²+bx+c=0, we get
a = 5, b = 19, c = -30
Discreminant (D)=b²-4ac
= (19)²-4×19×(-30)
= 361+600
= 961
By Quadratic Formula:
x = [-b±√D]/(2a)
= \frac{-19±\sqrt{961}}{2\times 5}
=\frac{-19±31}{10}
Now,
x= \frac{-19+31}{10}
Or x =\frac{-19-31}{10}
x = \frac{12}{10}\: Or\: x =\frac{-50}{10}
x = \frac{6}{5}\: Or \:x =-5