Question

(1/x+1) +(2/x+2)=(4/x+4) pls koi solve karo brainliest mark karungi

Answer 1

Answer:

x=2+2\sqrt{3}\:Or \: x=2-2\sqrt{3}

Step-by-step explanation:

\frac{1}{x+1}+\frac{2}{x+2}=\frac{4}{x+4}

\implies \frac{x+2+2(x+1)}{(x+1)(x+2)}=\frac{4}{x+4}

\implies \frac{x+2+2x+2)}{(x^{2}+3x+2)}=\frac{4}{x+4}

\implies \frac{3x+4}{x^{2}+3x+2}=\frac{4}{x+4}

\implies (3x+4)(x+4)=4(x^{2}+3x+2)

\implies 3x^{2}+12x+4x+16=4x^{2}+12x+8

\implies 3x^{2}+16x+16-4x^{2}-12x-8=0

\implies -x^{2}+4x+8=0

\implies x^{2}-4x-8=0

Compare \: this \: with \\ax^{2}+bx+c=0,we \:get

a=1,b=-4,x=-8

Discreminant (D)=b²-4ac

= (-4)²-4×1×(-8)

= 16+32

= 48

x = \frac{-b±\sqrt{D}}{2a}

=\frac{-(-4)±\sqrt{48}}{2}\\=\frac{4±4\sqrt{3}}{2}\\=2±2\sqrt{3}

\implies x=2+2\sqrt{3}\:Or \: x=2-2\sqrt{3}

Therefore,

x=2+2\sqrt{3}\:Or \: x=2-2\sqrt{3}