Question

If a -1/a =4, find the value of a2 + 1/a2
Pls answer fast I will mark brainliest

Answer 1

Answer:

18

Step-by-step explanation:

  We know ( a + b )^2 = a^2 + b^2 + 2ab

Square on both sides of a - 1/a = 4

⇒ ( a - 1 / a )^2 = 4^2

⇒ a^2 + ( 1 / a )^2 - 2( a * 1 / a ) = 16

⇒ a^2 + 1 / a^2 - 2( 1 ) = 16

⇒ a^2 + 1 / a^2 = 16 + 2

⇒ a^2 + 1 / a^2 = 18

     Hence the required value of a^2 + 1 / a^2 is 18

Answer 2

⠀⠀⠀⠀ $\purple{\mathbb{ANSWER}}$

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Given that:-

$\red{a - \frac{1}{a} = 4 }$

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$⇝ (a - \frac{1}{a}) {}^{2} = {(4)}^{2} \\⇝ {a }^{2} + \frac{1}{ {a}^{2} } - 2 \times a \times \frac{1}{a} = 16 \\ ⇝{a }^{2} + \frac{1}{ {a}^{2} } - 2 = 16 \\⇝ {a }^{2} + \frac{1}{ {a}^{2} } = 16 + 2 \\⇝ {a }^{2} + \frac{1}{ {a}^{2} } = 18$

∴ $\red{ {a }^{2} + \frac{1}{ {a}^{2} }= }$${\boxed{\red{ 18 }}}$