Question #92c75

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Answer 1 · 2017-01-30T18:18:17

#:. x=sqrt((bc)/a)[{y^((2a)/b)-(y+1)^((2a)/b)}/{y^((2a)/b)+(y+1)^((2a)/b)}]#

#{(1+xsqrt(a/(bc)))/(1-xsqrt(a/(bc)))}^(1/a)=(y/(y+1))^(2/b)#

Observe that, taking #a^(th)# power of both sides, the power of L.H.S. will become #(1/a)(a)=1#, & that of the R.H.S., #(2/b)(a)=(2a)/b#.

#{(1+xsqrt(a/(bc)))/(1-xsqrt(a/(bc)))}=(y/(y+1))^((2a)/b)=y^((2a)/b)/(y+1)^((2a)/b)#

Now, we use componendo-dividendo and get,

#{(1+xsqrt(a/(bc)))+(1-xsqrt(a/(bc)))}/{(1+xsqrt(a/(bc)))-(1-xsqrt(a/(bc)))}={y^((2a)/b)+(y+1)^((2a)/b)}/{y^((2a)/b)-(y+1)^((2a)/b)}#

#:. 1/{xsqrt(a/(bc))}={y^((2a)/b)+(y+1)^((2a)/b)}/{y^((2a)/b)-(y+1)^((2a)/b)}#

#:.{xsqrt(a/(bc))}={y^((2a)/b)-(y+1)^((2a)/b)}/{y^((2a)/b)+(y+1)^((2a)/b)}#

#:. x=sqrt((bc)/a)[{y^((2a)/b)-(y+1)^((2a)/b)}/{y^((2a)/b)+(y+1)^((2a)/b)}]#

Enjoy maths.!