Question

solve it plzz..... ​

Answer 1

Answer:

I think it is x=0another x is 6

0-1/6=5

Step-by-step explanation:

6minus into 0 =6 6 minus 1 =5

Answer 2

Question:

If $\displaystyle{\sf\:x\:-\:\dfrac{1}{x}\:=\:5}$, find the value of

$\displaystyle{\sf\:1\:.\:x^2\:+\:\dfrac{1}{x^2}}$

$\displaystyle{\sf\:2\:.\:x^4\:+\:\dfrac{1}{x^4}}$

Answer:

1. $\displaystyle{\boxed{\red{\sf\:x^2\:+\:\dfrac{1}{x^2}\:=\:27}}}$

2. $\displaystyle{\boxed{\red{\sf\:x^4\:+\:\dfrac{1}{x^4}\:=\:727}}}$

Step-by-step-explanation:

We have given that,

$\displaystyle{\sf\:x\:-\:\dfrac{1}{x}\:=\:5}$

We have to find the value of,

$\displaystyle{\sf\:1\:.\:x^2\:+\:\dfrac{1}{x^2}}$

$\displaystyle{\sf\:2\:.\:x^4\:+\:\dfrac{1}{x^4}}$

1.

Now,

$\displaystyle{\sf\:x\:-\:\dfrac{1}{x}\:=\:5}$

$\displaystyle{\implies\sf\:\left(\:x\:-\:\dfrac{1}{x}\:\right)^2\:=\:(\:5\:)^2\:\:\:-\:-\:-\:[\:Squaring\:both\:sides\:]}$

$\displaystyle{\implies\sf\:x^2\:-\:2\:\times\:\cancel{x}\:\times\:\dfrac{1}{\cancel{x}}\:+\:\left(\:\dfrac{1}{x}\:\right)^2\:=\:25\:\:\:-\:-\:-\:[\:\because\:(\:a\:-\:b\:)^2\:=\:a^2\:-\:2ab\:+\:b^2\:]}$

$\displaystyle{\implies\sf\:x^2\:-\:2\:+\:\dfrac{1}{x^2}\:=\:25}$

$\displaystyle{\implies\sf\:x^2\:+\:\dfrac{1}{x^2}\:=\:25\:+\:2}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x^2\:+\:\dfrac{1}{x^2}\:=\:27}}}}$

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2.

Now, we have

$\displaystyle{\sf\:x^2\:+\:\dfrac{1}{x^2}\:=\:27}$

$\displaystyle{\implies\sf\:\left(\:x^2\:+\:\dfrac{1}{x^2}\:\right)^2\:=\:(\:27\:)^2\:\:\:-\:-\:-\:[\:Squaring\:both\:sides\:]}$

$\displaystyle{\implies}\sf\:(\:x^2\:)^2\:+\:2\:\times\:\cancel{x^2}\:\times\:\dfrac{1}{\cancel{x^2}}\:+\:\left(\:\dfrac{1}{x^2}\:\right)^2\:=\:27\:\times\:27\:\:\:-\:-\:-\:[\:\because\:(\:a\:+\:b\:)^2\:=\:a^2\:+\:2ab\:+\:b^2\:]$

$\displaystyle{\implies\sf\:x^2\:\times\:x^2\:+\:2\:+\:\left(\:\dfrac{1}{x^2\:\times\:x^2}\:\right)\:=\:729}$

$\displaystyle{\implies\sf\:x^{2\:+\:2}\:+\:2\:+\:\left(\:\dfrac{1}{x^{2\:+\:2}}\:\right)\:=\:729\:\:\:-\:-\:-\:[\:\because\:a^m\:\times\:a^n\:=\:a^{m\:+\:n}\:]}$

$\displaystyle{\implies\sf\:x^4\:+\:2\:+\:\dfrac{1}{x^4}\:=\:729}$

$\displaystyle{\implies\sf\:x^4\:+\:\dfrac{1}{x^4}\:=\:729\:-\:2}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x^4\:+\:\dfrac{1}{x^4}\:=\:727}}}}$