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Solve the equation and verify your answer:((x+1)/(x-4))2 = (x+8)/(x-2) |
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Answer» We have, ((x+1)/(x-4))2 = (x+8)/(x-2) (x+1)2 / (x-4)2 – (x+8) / (x-2) = 0 By taking LCM as (x-4)2 (x-2) ((x+1)2 (x-2) – (x+8) (x-4)2) / (x-4)2 (x-2) = 0 By cross-multiplying we get, (x+1)2 (x-2) – (x+8) (x-4)2 = 0 Upon expansion we get, (x2 + 2x + 1) (x-2) – ((x+8) (x2 – 8x + 16)) = 0 x3 + 2x2 + x – 2x2 – 4x – 2 – (x3 – 8x2 + 16x + 8x2 – 64x + 128) = 0 x3 + 2x2 + x – 2x2 – 4x – 2 – x3 + 8x2 – 16x – 8x2 + 64x – 128 = 0 45x – 130 = 0 x = 130/45 = 26/9 Now let us verify the given equation, ((x+1)/(x-4))2 = (x+8)/(x-2) (x+1)2 / (x-4)2 = (x+8) / (x-2) By substituting the value of ‘x’ we get, (26/9 + 1)2 / (26/9 – 4)2 = (26/9 + 8) / (26/9 – 2) ((26+9)/9)2 / ((26-36)/9)2 = ((26+72)/9) / ((26-18)/9) (35/9)2 / (-10/9)2 = (98/9) / (8/9) (35/-10)2 = (98/8) (7/2)2 = 49/4 49/4 = 49/4 Hence, the given equation is verified. |
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