Question

PLS HELP!! 1. if [x-1/x]=5, then the value of [x2+1/x2] is [here~x2=xsquare

(a)25 (b)27 (c)29 (d)none of these


2.if{x-1/x}=5, then the value of {x4+1/x4} is
(a)725 (b)727 (c)729 (d)none of these

Answer 1

1 - 27 , 2- 727

Explanation:

see image for explanation

Answer 2

1. (b)

2. (b)

Explanation:

1.

We have,

`x-(1)/(x)=5`

Now, squaring both sides, we get

`(x-(1)/(x)) ^(2)=5^(2)` .......(1)

Now, using the identity
`(a-b)^2=a^2+b^2-2ab` in the LHS of the equation (1), we get

`x^(2) +(1)/(x^2)-2* x *(1)/(x)=25`

⇒
`x^2+(1)/(x^2)-2=25`

⇒
`x^(2) +(1)/(x^2)=25+2=27`

∴ The correct answer is option (b).

2.

We have,

`x-(1)/(x)=5`

Now, squaring both sides, we get

`(x-(1)/(x)) ^(2)=5^(2)` .......(1)

Now, using the identity
`(a-b)^2=a^2+b^2-2ab` in the LHS of the equation (1), we get

`x^(2) +(1)/(x^2)-2* x *(1)/(x)=25`

⇒
`x^2+(1)/(x^2)-2=25`

⇒
`x^(2) +(1)/(x^2)=25+2=27` .......(2)

Again, squaring both sides of equation (2), we get

`(x^2+(1)/(x^2))^2=(27)^2` .......(3)

Now, using the identity
`(a+b)^2=a^2+b^2+2ab` in the LHS of the

equation (3), we get

`(x^2)^2+((1)/(x^2))^2+2* x^2* (1)/(x^2)=729`

⇒
`x^4+(1)/(x^4)+2=729`

⇒
`x^4+(1)/(x^4)=729-2=727`

∴ The correct answer is option (b).