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