Math, asked by Anonymous, 3 months ago

a² + 1/a² = 27
a - 1/a = ?
nEED Tq!~

Answers

Answered by XxItsDivYanShuxX
3

\LARGE\bold{\color{yellow}{\underline{\mathtt{\color{magenta}{Given:↓}}}}}

  • \large\bold{a² +  \frac{1}{ {a}^{2} }  = 27}

\LARGE\bold{\color{magenta}{\underline{\mathtt{\color{yellow}{Find:↓}}}}}

  •  \large \bold{a -  \frac{1}{ {a}^{2} }  = ?}

\LARGE\bold{\color{yellow}{\underline{\mathtt{\color{navy}{Solution:↓}}}}}

It is given that,

a² +  \frac{1}{ {a}^{2} }  =  \bold{27}

So, by subtracting both the sides we get:

 {a}^{2}  - 2 = 27 - 2

 \implies {a}^{2}  - 2 \times a \times ( \frac{1}{a} ) +  \frac{1}{ {a}^{2} }  = 25

 \implies(a -  \frac{1}{ {a}^{2} } ) = 25

 \implies (a -  \frac{1}{a} ) =  \sqrt{25}

 \therefore(a -  \frac{1}{a} ) =  \large \bold{ \color{yellow}{ \boxed {\displaystyle{\underline{ + } 5}}}}

Hence, \bold{(a -  \frac{1}{a} ) =  \large \bold{ \color{lime}{ \boxed {\displaystyle{ + } 5}}}}

______________________

Hopes its helpful.

Answered by CopyThat
49

Answer:

  • ±5

Step-by-step explanation:

Given

  • a² + 1/a² = 27

To find

  • a - 1/a

Solution

→ (a - 1/a)² = a² + 1/a² - 2

  • (a - 1/a)² = 27 - 2
  • (a - 1/a)² = 25
  • (a - 1/a) = √25
  • (a - 1/a) = ±5

Hence, the value of a - 1/a is ±5.

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