Solve the equation 5xx√8x−1=500 find the rational root .
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Solution
Given equation 5xx√8x−1=500 ⇒5x.8(x−1x)=53.22 ⇒5x.23x−3x=53.22 5x−3.2(x−3x)=1 (5.21/x)(x−3)=1 ⇒(x−3)log(5.21/x)=0 ⇒x−3=0,log(5.21/x)=0 ∴x1=3,5.21/x=1 ⇒21/x=(1/5) ∴x2=−log52 Hence roots of the original equation are x1=3 and x2=−log52