Question

find x satisfying 1/(x+1) + 2/(x+2) = 4/(x+4)​

Answer 1

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Answer 2

Answer:

$= > \frac{1}{x + 1} + \frac{2}{x + 2} = \frac{4}{x + 4} \\ = > \frac{1(x + 2) + 2(x + 1)}{(x + 1)(x + 2)} = \frac{4}{x + 4} \\ = > \frac{x + 2 + 2x + 2}{{x}^{2} + 2x + x + 2} = \frac{4}{x + 4} \\ = > \frac{3x + 4}{ {x}^{2} + 3x + 2 } = \frac{4}{x + 4} \\ = > (3x + 4)(x + 4) = 4( {x}^{2} + 3x + 2) \\ = > 3 {x}^{2} + 12x + 4x + 16 = 4 {x}^{2} + 12x + 8 \\ = >( 4 - 3) {x}^{2} + (12 - 12 - 4)x + (8 - 16) = 0 \\ = > {x}^{2} - 4x - 8 = 0$

$= > d = {b}^{2} - 4ac \\ = > d = {( - 4)}^{2} - (4 \times 1 \times - 8) \\ = > d = 16 + 32 = 48$

$= > x = \frac{ - b \frac{ + }{ - } \sqrt{d} }{2a} = \frac{ - b \frac{ + }{ - } \sqrt{48} } {2a} = \frac{ 4 \frac{ + }{ - }4 \sqrt{2} }{2} = 2 \frac{ + }{ - } 2 \sqrt{3}$

$\sqrt{3} = 1.73$

$x = 2 \frac{ + }{ - } 2 \times 1.73 = 2 \frac{ + }{ - }3.4 6$

Therefore,

$x = 2 + 3.46 = 5.46 \\ or \\ x = 2 - 3.46 = - 1.46$

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