Question

solve the equation
$find \: the \: value \: of \: {x}^{3} + \frac{1}{ {x}^{3} } + 2 \: for \: x = 2$
2). find the value of p³q³ - 9p²q² + 20pq for p =3 , q = 1.​

Answer 1

$ans \: 1). \: = {x}^{3} + \frac{1}{ {x}^{3} } + 2 \: \: \: \: \: \: x = 2 \\ = ( {2}^{3} ) + \frac{1}{( {2}^{3})} + 2 \\ = 8 + \frac{1}{8} + 8 \\ = \frac{64 + 1 + 16}{8} \\ = \frac{81}{8}$

Ans 2). = p³q³ - 9 p²q² + 20pq

= 3³×1³ - 9× 3²× 1² + 20 × 3 × 1

= 27×1 - 9×9×1 + 60×1

= 27 - 81 × 1 + 60

= -54 + 60

= 6

Answer 2

$\huge \sf \bf\color{purple}\underline{\underline{Solution}} :$

$\sf \large Equation \\ x^{3} + \frac{1}{ {x}^{3} } + 2$

$= {x}^{3} + \frac{1}{ {x}^{3} } + 2 \: \: \: \: \: \: x = 2 \\ = ( {2}^{3} ) + \frac{1}{( {2}^{3})} + 2 \\ = 8 + \frac{1}{8} + 8 \\ = \frac{64 + 1 + 16}{8} \\ = \boxed{\frac{81}{8}}$

$\\ \sf Equation \\ p³q³ - 9p²q² + 20pq$

Ans 2). = p³q³ - 9 p²q² + 20pq

$\implies$3³×1³ - 9× 3²× 1² + 20 × 3 × 1

$\implies$27×1 - 9×9×1 + 60×1

$\implies$27 - 81 × 1 + 60

$\implies$-54 + 60

$\implies \boxed{6}$