Question

please solve this fast please

Answer 1

One hundred seventy one plus forty five root fifteen

Answer 2

Answer: $126\sqrt{15}$

Step-by-step explanation:

$x = 4 + \sqrt{15}$

$1/x = 1/(x = 4 - \sqrt{15})$

By using rationalisation

$1/x = 1/(4 + \sqrt{15}) * [(4 - \sqrt{15})/(4 - \sqrt{15})]\\ 1/x = (4 - \sqrt{15})/(4^{2} - (\sqrt{15})^{2} )\\ 1/x= (4 - \sqrt{15})/(16 - 15 )\\ 1/x = (4 - \sqrt{15})/1\\1/x = (4 - \sqrt{15})$

$x^{2} + (1/x)^{2} = (x - 1/x)^{2} + 2$

                  = $[4 + \sqrt{15} - (4 - \sqrt{15})]^{2} + 2$

                  = $[4 + \sqrt{15} - 4 + \sqrt{15}]^{2} + 2$

                  = $(2\sqrt{15} )^{2} + 2$

                  = 60 + 2

                  = 62

Now,

$x^{3} - (1/x)^{3} = [x - (1/x)][x^{2} + (1/x)^{2} + x(1/x)]\\x^{3} - (1/x)^{3} = [4+\sqrt{15} - (4-\sqrt{15})][62 + 1]\\x^{3} - (1/x)^{3} = [4+\sqrt{15} - 4+\sqrt{15}][63]\\x^{3} - (1/x)^{3} = [2\sqrt{15}][63]\\x^{3} - (1/x)^{3} = [2\sqrt{15}][63]\\x^{3} - (1/x)^{3} = 126\sqrt{15}$