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,

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

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

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

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

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