Answer:
1. (b)
2. (b)
Step-by-step explanation:
1.
We have,
![x-\frac{1}{x}=5](https://tex.z-dn.net/?f=x-%5Cfrac%7B1%7D%7Bx%7D%3D5)
Now, squaring both sides, we get
.......(1)
Now, using the identity
in the LHS of the equation (1), we get
⇒![x^2+\frac{1}{x^2}-2=25](https://tex.z-dn.net/?f=x%5E2%2B%5Cfrac%7B1%7D%7Bx%5E2%7D-2%3D25)
⇒![x^{2} +\frac{1}{x^2}=25+2=27](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%5Cfrac%7B1%7D%7Bx%5E2%7D%3D25%2B2%3D27)
∴ The correct answer is option (b).
2.
We have,
![x-\frac{1}{x}=5](https://tex.z-dn.net/?f=x-%5Cfrac%7B1%7D%7Bx%7D%3D5)
Now, squaring both sides, we get
.......(1)
Now, using the identity
in the LHS of the equation (1), we get
⇒![x^2+\frac{1}{x^2}-2=25](https://tex.z-dn.net/?f=x%5E2%2B%5Cfrac%7B1%7D%7Bx%5E2%7D-2%3D25)
⇒
.......(2)
Again, squaring both sides of equation (2), we get
.......(3)
Now, using the identity
in the LHS of the
equation (3), we get
![(x^2)^2+(\frac{1}{x^2})^2+2\times x^2\times \frac{1}{x^2}=729](https://tex.z-dn.net/?f=%28x%5E2%29%5E2%2B%28%5Cfrac%7B1%7D%7Bx%5E2%7D%29%5E2%2B2%5Ctimes%20x%5E2%5Ctimes%20%5Cfrac%7B1%7D%7Bx%5E2%7D%3D729)
⇒![x^4+\frac{1}{x^4}+2=729](https://tex.z-dn.net/?f=x%5E4%2B%5Cfrac%7B1%7D%7Bx%5E4%7D%2B2%3D729)
⇒![x^4+\frac{1}{x^4}=729-2=727](https://tex.z-dn.net/?f=x%5E4%2B%5Cfrac%7B1%7D%7Bx%5E4%7D%3D729-2%3D727)
∴ The correct answer is option (b).