Question

of x2 + 1/x = 4 find the value of 2x3 + 2/x3​

Answer 1

Answer:

x2+1/x=4,x=2, 2x3+2/x3=6.33

Answer 2

Answer:

${x}^{2} + \frac{1}{ {x}^{2} } = 4 \\{x}^{2} + \frac{1}{ {x}^{2} } + 2 = 6 \\ {(x + \frac{1}{x} )}^{2} = 6 \\ x + \frac{1}{x} = \sqrt{6}$

So,

${x}^{3}+\frac{1}{{x}^{3}} = (x + \frac{1}{x})( {x}^{2} + \frac{1}{ {x}^{2} } - x. \frac{1}{x} )$

${x}^{3}+\frac{1}{{x}^{3}} = \sqrt{6} (4 - 1 )$

${x}^{3}+\frac{1}{{x}^{3}} = 3\sqrt{6}$

So,

$2{x}^{3}+\frac{1}{2{x}^{3}} = 6\sqrt{6}$