Question

If x=(4 - root 15), find the value of x + 1/x​

Answer 1

Answer:

4

X=(4-√15)

x+1/X=. 4-√15+1/(√15)

=(√15×4)-15+15

-------------------

√15

=. 4

(:-. -15+15=0)

√15*√15=15

Answer 2

Question:-

• If x=(4 - root 15), find the value of x + 1/x

Solution:-

$\small\sf\underline\green{given}$ ⟼x=4-√15

$\small\sf\underline\green{need\:to\:find}$⟼x+1/x

______________________________________

$x = 4 - \sqrt{15}$

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

By rationalizing the denominator ,we get as

$\frac{1}{4 - \sqrt{15} } \times \frac{4 + \sqrt{15} }{4 + \sqrt{15} }$

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

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

$= 4 + \sqrt{15}$

Now, after rationalizing the denominator we need to find the value of x+1/x

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

$x + \frac{1}{x} = 4 + 4 = 8$

Hence, the value of x+1/x is $\huge\sf\underline\red{8}$

______________________________________