P ProdigaI New member Joined Jun 13, 2009 Messages 7 Jun 13, 2009 #1 x^-2 - 8x^-1 + 12 = 0 x to the negative 2 power minus 8x to the negative 1 power plus 12 equals 0 Thanks
x^-2 - 8x^-1 + 12 = 0 x to the negative 2 power minus 8x to the negative 1 power plus 12 equals 0 Thanks
S soroban Elite Member Joined Jan 28, 2005 Messages 5,584 Jun 13, 2009 #2 Hello, ProdigaI! \(\displaystyle \text{Solve: }\;x^{-2} - 8x^{-1} + 12 \:=\: 0\) Click to expand... \(\displaystyle \text{Multiply by }x^2\!:\quad 1 - 8x + 12x^2 \:=\:0\quad\Rightarrow\quad 12x^2 - 8x + 1 \:=\:0\) . . \(\displaystyle \text{which factors: }\;(2x - 1)(6x - 1) \:=\;0\) . . \(\displaystyle \text{and has roots: }\;x \:=\:\tfrac{1}{2},\:\tfrac{1}{6}\)
Hello, ProdigaI! \(\displaystyle \text{Solve: }\;x^{-2} - 8x^{-1} + 12 \:=\: 0\) Click to expand... \(\displaystyle \text{Multiply by }x^2\!:\quad 1 - 8x + 12x^2 \:=\:0\quad\Rightarrow\quad 12x^2 - 8x + 1 \:=\:0\) . . \(\displaystyle \text{which factors: }\;(2x - 1)(6x - 1) \:=\;0\) . . \(\displaystyle \text{and has roots: }\;x \:=\:\tfrac{1}{2},\:\tfrac{1}{6}\)
D Deleted member 4993 Guest Jun 13, 2009 #3 ProdigaI said: x^-2 - 8x^-1 + 12 = 0 x to the negative 2 power minus 8x to the negative 1 power plus 12 equals 0 Thanks Click to expand... substitute: u = 1/x then u^2 - 8u + 12 = 0 (u -6)(u-2) = 0 u = 2 converts to x = 1/2 and u = 6 converts to x = 1/6
ProdigaI said: x^-2 - 8x^-1 + 12 = 0 x to the negative 2 power minus 8x to the negative 1 power plus 12 equals 0 Thanks Click to expand... substitute: u = 1/x then u^2 - 8u + 12 = 0 (u -6)(u-2) = 0 u = 2 converts to x = 1/2 and u = 6 converts to x = 1/6
