Solving for XDate: 01/13/97 at 03:51:08 From: Yaroslav Greshilov Subject: Equation I need help with this very much. Sorry, my English is not very good because I'm Russian, but I hope you will help me. 3(x*x)-2x+2 = 2/(3(x*x)-2x+1) Find answers to this equation. Date: 01/13/97 at 13:26:51 From: Doctor Rob Subject: Re: Equation Thanks for your question. Your English is good enough, and certainly a lot better than my Russian! I can think of two ways to solve this equation: A) Let y = 3*x^2 - 2*x, so that the equation reads: y + 2 = 2/(y + 1) Now multiply both sides by (y + 1): (y + 2)*(y + 1) = 2 Subtract 2 from both sides, and expand: y^2 + 3*y + 2 - 2 = 0 y^2 + 3*y = 0 y*(y + 3) = 0 y = 0 or y = -3 Now put these equations in y in terms of x: 3*x^2 - 2*x = 0 or 3*x^2 - 2*x = -3 x*(3*x - 2) = 0 or 3*x^2 - 2*x + 3 = 0 x = 0 or x = 2/3 or x = (1 + 2*Sqrt[-2])/3 or x = (1 - 2*Sqrt[-2])/3 B) Multiply both sides by the denominator on the right, bring all terms to the left side, expand and gather like terms. You will have a fourth degree equation. Factor the left side and set each factor equal to zero and solve for x in each part. If you need more help, write back again. -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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