Question

If a + 1/a = 17/4, find the value of (a- 1/a)

Answer 1

Answer:

Your Answer is:

Step-by-step explanation:

$\frac{a^{2} + 1 }{a} = \frac{17}{4}\\ Therefore,\\a^{2} + 1 = \frac{17 a}{4}$

Further we get;

a^2 - 17a/4 +1 = 0

By splitting the middle terms

Answer 2

Answer:

+/- $\frac{15}{4}$

Step-by-step explanation:

$a + \frac{1}{a} = \frac{17}{4} \\\\To find$

$(a- \frac{1}{a})$

$(a + \frac{1}{a} )^{2}$ $= a^{2} +$$\frac{1}{a^{2} }$ $+ 2$

$\frac{17}{4}^{2}$ =$\frac{289}{16}$ $= a^{2} +$$\frac{1}{a^{2} }$ $+ 2$ ⇒ $a^{2} + \frac{1}{a^{2} }$ = $\frac{257}{16}$

$(a-\frac{1}{a} )^{2}$ =  $a^{2} +\frac{1}{a^{2} } - 2$ ⇒ $(a-\frac{1}{a} )^{2}$ = $\frac{257}{16}$ - 2

⇒$(a-\frac{1}{a} )^{2}$ = $\frac{225}{16}$

⇒$a-\frac{1}{a}$ = √$\frac{225}{16}$

⇒+/- $\frac{15}{4}$