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Solve the equation and verify your answer: ((x+1)/(x+2))2 = (x+2) / (x + 4) |
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Answer» We have, ((x+1)/(x+2))2 = (x+2) / (x + 4) (x+1)2 / (x+2)2 – (x+2) / (x + 4) = 0 By taking LCM as (x+2)2 (x+4) ((x+1)2 (x+4) – (x+2) (x+2)2) / (x+2)2 (x+4) = 0 By cross-multiplying we get, (x+1)2 (x+4) – (x+2) (x+2)2 = 0 Let us expand the equation (x2 + 2x + 1) (x + 4) – (x + 2) (x2 + 4x + 4) = 0 x3 + 2x2 + x + 4x2 + 8x + 4 – (x3 + 4x2 + 4x + 2x2 + 8x + 8) = 0 x3 + 2x2 + x + 4x2 + 8x + 4 – x3 – 4x2 – 4x – 2x2 – 8x – 8 = 0 -3x – 4 = 0 x = -4/3 Now let us verify the given equation, ((x+1)/(x+2))2 = (x+2) / (x + 4) By substituting the value of ‘x’ we get, (x+1)2 / (x+2)2 = (x+2) / (x + 4) (-4/3 + 1)2 / (-4/3 + 2)2 = (-4/3 + 2) / (-4/3 + 4) ((-4+3)/3)2 / ((-4+6)/3)2 = ((-4+6)/3) / ((-4+12)/3) (-1/3)2 / (2/3)2 = (2/3) / (8/3) 1/9 / 4/9 = 2/3 / 8/3 1/4 = 2/8 1/4 = 1/4 Hence, the given equation is verified. |
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