Question

If x + √15 = 4. Then x + 1/x =
Please solve and explain...

Answer 1

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Answer 2

Answer:

$x+\frac{1}{x}=8$

Step-by-step explanation:

Given : If $x+\sqrt{15}=4$

To find : The value of $x+\frac{1}{x}$

Solution :

$x+\sqrt{15}=4$

$x=4-\sqrt{15}$

$\frac{1}{x}=\frac{1}{4-\sqrt{15}}$

Substitute in $x+\frac{1}{x}$

$x+\frac{1}{x}=4-\sqrt{15}+\frac{1}{4-\sqrt{15}}$

$x+\frac{1}{x}=\frac{(4-\sqrt{15})^2+1}{4-\sqrt{15}}$

$x+\frac{1}{x}=\frac{16+15-8\sqrt{15}+1}{4-\sqrt{15}}$

$x+\frac{1}{x}=\frac{32-8\sqrt{15}}{4-\sqrt{15}}$

$x+\frac{1}{x}=\frac{8(4-\sqrt{15})}{4-\sqrt{15}}$

$x+\frac{1}{x}=8$

Therefore, The value of $x+\frac{1}{x}=8$