Question-80912

Question Number 80912 by TawaTawa last updated on 07/Feb/20

Commented by john santu last updated on 08/Feb/20

\frac{x^{4}}{q^{3}} + \frac{y^{4}}{p^{3}} = 1

\Rightarrow {(\frac{x^{4}}{q^{3}}) + (\frac{y^{4}}{p^{3}})} \times {(\frac{x^{2}}{q^{3}}) + (\frac{y^{2}}{p^{3}})} =

\frac{x^{6}}{q^{6}} + \frac{x^{4} y^{2}}{p^{3} q^{3}} + \frac{x^{2} y^{4}}{p^{3} q^{3}} + \frac{y^{6}}{p^{6}} = \frac{x^{2}}{q^{3}} + \frac{y^{2}}{p^{3}}

\frac{x^{6}}{q^{6}} + \frac{y^{6}}{p^{6}} + \frac{x^{2} y^{2} (x^{2} + y^{2})}{p^{3} q^{3}} = \frac{x^{2} p^{3} + y^{2} q^{3}}{p^{3} q^{3}}

\frac{x^{6}}{q^{6}} + \frac{y^{6}}{p^{6}} = \frac{x^{2} p^{3} + y^{2} q^{3} - x^{2} y^{2}}{p^{3} q^{3}} (1)

(2) (x^{2} + y^{2}) \times (p^{3} + q^{3}) = 1

\Rightarrow x^{2} p^{3} + x^{2} q^{3} + y^{2} p^{3} + y^{2} p^{3} = 1

x^{2} p^{3} + y^{2} q^{3} = 1 - x^{2} q^{3} - y^{2} p^{3}

s u b s t i t u t e (2) i n (1)

\Rightarrow \frac{x^{6}}{q^{6}} + \frac{y^{6}}{p^{6}} = \frac{1 - x^{2} q^{3} - y^{2} p^{3} - x^{2} y^{2}}{p^{3} q^{3}}

Commented by TawaTawa last updated on 08/Feb/20

God bless you sir