Question

if a+1/a=17/4 find (a-1/a) plz tell ​

Answer 1

Step-by-step explanation:

let

a+1/a =17/5

a-1/a. =

$\sqrt{17 \div 5} ) { }^{2} - 4$

$\sqrt{289} \div 25 - 4$

$\sqrt{289 - 100} \div 25$

$\sqrt{189 \div 25} \: answer$

Answer 2

❥︎Question :-

$\bf \:a + \dfrac{1}{a} = \dfrac{17}{4} \: then \: find \: a - \dfrac{1}{a}$

$\bf \:\large \red{AηsωeR } ✍$

❥︎Given :-

$\bf \:a + \dfrac{1}{a} = \dfrac{17}{4}$

❥︎To Find :-

$\bf \:a - \dfrac{1}{a}$

❥︎Identity used :-

$\bf \: {(x + y)}^{2} - {(x - y)}^{2} = 4xy$

❥︎Solution :-

$\bf \:a + \dfrac{1}{a} = \dfrac{17}{4}$

Using Identity,

$\bf \: {(x + y)}^{2} - {(x - y)}^{2} = 4xy$

$\bf \: ⟼ Put \: x = a \: and \: y = \dfrac{1}{a} \: we \: get$

$\bf \: ⟼ {(a + \dfrac{1}{a} )}^{2} - {(a - \dfrac{1}{a} )}^{2} = 4 \times a \times \dfrac{1}{a}$

$\bf \: ⟼ {(\dfrac{17}{4} )}^{2} - {(a - \dfrac{1}{a}) }^{2} = 4$

$\bf \: ⟼ \dfrac{289}{4} - {(a - \dfrac{1}{a}) }^{2} = 4$

$\bf \: ⟼ {(a - \dfrac{1}{a}) }^{2} = \dfrac{289}{16} - 4$

$\bf \: ⟼ {(a - \dfrac{1}{a}) }^{2} = \dfrac{289 - 64}{16}$

$\bf \: ⟼ {(a - \dfrac{1}{a}) }^{2} = \dfrac{225}{16}$

$\bf \: ⟼ a - \dfrac{1}{a} = \dfrac{15}{4}$

__________________________________________

$\large \red{\bf \: ⟼ Explore \: more } ✍$

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• a² - b² = (a + b)(a - b)