Find no. of solutions of \(\large(x^2-7x+11)^{(x-6)(x-5)}=x\)

Please upload solution if u can

Find no. of solutions of \(\large(x^2-7x+11)^{(x-6)(x-5)}=x\)

Please upload solution if u can

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewestTaking log both sides,

\((x-5)(x-6)\ln (x^2-7x+11)=\ln x\)

Note that \(x=5\) is a repeated root so the differential would be 0 at \(x=5\). Try to plot the graph. At \(x=\infty,\ LHS=\infty\). At \(x=5,6,2\), \(LHS=0\). At \(x=0,\ LHS>0\). I think graphs can be plotted now and it will intersect \(y=\ln x\) at two points. – Pranjal Jain · 2 years, 8 months ago

Log in to reply

@Chew-Seong Cheong @Aneesh Kundu @Pranjal Jain @megh choksi @Jon Haussmann @Trevor Arashiro @Trevor B. @Calvin Lin @Aman Sharma Please upload solution if u can – Mehul Chaturvedi · 2 years, 8 months ago

Log in to reply

– Trevor Arashiro · 2 years, 8 months ago

I'll post more tomorrow, but for now, I'd just say to create a sign chart of where the exponent and where the \(x^2-7x+11\) are positive and when negative and where the LHS exceeds the RHS. The problem is that if the LHS intersects the RHS when negative, You have to watch for extraneous solutions because \((-2)^{\frac{7}{12}}\) is not an answer since its imaginary (the answer isn't 2^7/12, Im just using it as an example.Log in to reply