Question

a - 1/a = 6, then find a² + 1/a²
please answer it step by step
and it's correct answer will be 38 so please answer it step by step​

Answer 1

Answer:

Given :-

${ \boxed{ \red{ \tt { \bullet \: \: {a - \dfrac{1}{a} = 6}}}}}$

To Find :-

$\sf \: {a}^{2} + \dfrac{1}{ {a}^{2} }$

Solution :-

At first squaring both sides

$\sf \bigg \lgroup \: a - \dfrac{1}{a} \bigg \rgroup^{2} = {6}^{2}$

Apply Identity

(a - b)² = a² - 2ab + b²

$\tt \: {a}^{2} - 2(a) \bigg( \dfrac{1}{a} \bigg) + \dfrac{1}{ {a}^{2} } = 36$

$\tt \: {a}^{2} - 2 \times \cancel{a} \times \dfrac{1}{ \cancel a \: } + \dfrac{1}{ {a}^{2} } = 36$

$\tt \: {a}^{2} - 2 + \dfrac{1}{ {a}^{2} } = 36$

$\sf \: {a}^{2} + \dfrac{1}{ {a}^{2} } = 36 + 2$

${ \boxed { \red{ \underline{ \bf {a}^{2} + \dfrac{1}{ {a}^{2} } = 38}}}}$

Answer 2

Answer:

+-5√29 is the Answer.

Step-by-step explanation:

supposed to be the right answer in one method

1. If a-1/a=5 the a-1=5a

2. -1=5a-a which is -1=4a which is a=-1/4 ————1

3. a²-1/a² is (-1/4)² -1/(-1/4)² which is 1/16 -1/1/16.

• -15/16 / 1/16

• Applying another method from given condition in problem.

• Other right answer is a-1/a=5—Eq1

• So squaring both sides

• We get a² -2a/a +1/a² which is a² +1/a² -2=5×5

• Which further is a²+1/a²-2=25—Eq2

• Now adding 4 to both sides

• a²+1/a²-2+4=25+4

•Which is a²+2+1/a²=29

• Further square root of both sides

• √a²+2+1/a²=√29

• a+1/a=√29

• Now in problem the then asked what is a²-1/a² is (a+1/a)(a-1/a)

• a+1/a ×a-1/a

• Whereas in question a-1/a=5 and a+1/a=√29 is proved

• So +-5√29 is Answer.

Hope this helps you.

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