Question

if (a^2+1/a^2) =14,find the value of (a^2-1/a^2)​

Answer 1

Answer:

here is your answer mate

Step-by-step explanation:

a² + \dfrac{1}{ {a}^{2} }a21 = 14

__________ [GIVEN]

We have to find a³ + \dfrac{1*}{{a}^{3}}a31∗

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Solution:

=> a² + \dfrac{1}{ {a}^{2} }a21 = 14

• Add 2 on both sides.

=> a² + \dfrac{1}{ {a}^{2} }a21 + 2 = 14 + 2

• We can also write this equal like..

=> a² + \dfrac{1}{ {a}^{2} }a21 + 2 \dfrac{a}{a}aa = 16

We know that

a² + b² + 2ab = (a + b)²

So..

=> ({a \: + \: \dfrac{1}{a}) }^{2}(a+a1)2 = (4)²

=> a + \dfrac{1}{a}a1 = { (\sqrt{4}) }^{2}(4)2

=> a + \dfrac{1}{a}a1 = 4

• Now cube on both sides.

=> ({a \: + \: \dfrac{1}{a}) }^{3}(a+a1)3 = (4)³

=> a³ + \dfrac{1}{ {a}^{3} }a31 + 3(\dfrac{a}{a})(aa) (a \: + \: \dfrac{1}{a})(a+a1) = 64

=> a³ + \dfrac{1}{ {a}^{3} }a31 + 3 (a \: + \: \dfrac{1}{a} )(a+a1) = 64

=> a³ + \dfrac{1}{ {a}^{3} }a31 + 3(4) = 64

=> a³ + \dfrac{1}{ {a}^{3} }a31 = 64 - 12

______________________________

a³ + \dfrac{1}{ {a}^{3} }a31 = 52

__________ [ANSWER]