Question

If x = 2+3√2, then find the value of x + 14

x​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

$6\sqrt{2}$

Step-by-step explanation:

x=$2$+$3\sqrt{2}$

$\frac{14}{x} = \frac{14}{2+3\sqrt{2} } \\ = \frac{14( 2- 3\sqrt{2}) }{(2^{2}-3\sqrt{2^{2} } )} \\= \frac{28-42\sqrt{2}}{4-18} \\=\frac{28-42\sqrt{2} }{-14}\\ =\frac{14(2-3\sqrt{2} )}{-14} \\= -(2-3\sqrt{2} )\\=-2+3\sqrt{2}$

now,

$x+\frac{14}{x} \\=2+3\sqrt{2} +[ (-2)+3\sqrt{2} ]\\=2+3\sqrt{2} -2+3\sqrt{2}\\ =6\sqrt{2}$