Question

if x and y are positive real numbers such that 216x³ - 343y³ =1385 and 6x²y - 7x²y = 10 , then find the value of 6x - 7y​

Answer 1

Answer:

$216x {}^{3} - 343y { }^{3} = 1385 \: and \: \\ 6x {}^{2} y - 7x {}^{2} y = 10 \\ ie \: x {}^{2} y = - 10 \\ now \: y = (- 10 \div x {}^{2} ) \\ hence \: 216x {}^{3} \times ( - 10 \div x {}^{2} ) - 343 \times ( - 10 \div x {}^{2} ) {}^{3} = 1385 \\ - 2160 x +(343000 \div x {}^{6} ) = 1385 \\ 2160x {}^{7} - 343000 = - 1385 x {}^{6} \\2160x {}^{7} + 1385x {}^{6} - 343000 = 0 \\ from \: here \: find \: the \: roots \: of \: this \: quadratic \: equation \: once \: the \: root \: found \: substitute \: in \: above \: equation \: and \: find \: y \\ finly \: put \: the \: value \: of \: x \: and \: y \: the \: required \: answer \: will \: come \: out.$