For a Given Number, Solve the Expression...From: Anonymous Date: Fri, 28 Jun 1996 9:22:58 -0400 (EDT) Subject: Solve the expression I don't understand this problem. Can you help me? For a given number m, m greater than or equal to 1 , solve: The square root of m + x plus the square root of m - x divided by the square root of m. Date: Fri, 28 Jun 1996 13:33:35 -0400 (EDT) From: Dr. Anthony Subject: Re: Solve the expression Start by multiplying through by the denominator to get: sqrt(m+x) + sqrt(m-x) = sqrt(m){sqrt(m+x) - sqrt(m-x)} Now square both sides using (a+b)^2 = a^2 + 2ab + b^2 to get after collecting terms: 2m + 2sqrt(m+x)*sqrt(m-x) = m{2m - 2sqrt(m+x)*sqrt(m-x)} cancel 2's and collect the sqrt(m+x)*sqrt(m-x) to one side: sqrt(m+x)*sqrt(m-x){1+m} = m^2 - m sqrt(m+x)*sqrt(m-x) = m(m-1)/(m+1) Now square both sides again (m+x)(m-x) = m^2(m-1)^2/(m+1)^2 m^2 - x^2 = m^2(m-1)^2/(m+1)^2 x^2 = m^2 - m^2(m-1)^2/(m+1)^2 = {m^2(m+1)^2 - m^2(m-1)^2}/(m+1)^2 so x^2 = 4m^3/(m+1)^2 and x = +or- 2m*sqrt(m)/(m+1) -Doctor Anthony, The Math Forum |
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