Question

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

Answer 1

Answer:

1 - 27 , 2- 727

Step-by-step explanation:

see image for explanation

Answer 2

Answer:

1. (b)

2. (b)

Step-by-step explanation:

1.

We have,

$x-\frac{1}{x}=5$

Now, squaring both sides, we get

   $(x-\frac{1}{x}) ^{2}=5^{2}$        .......(1)

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

  $x^{2} +\frac{1}{x^2}-2\times x \times\frac{1}{x}=25$

⇒$x^2+\frac{1}{x^2}-2=25$

⇒$x^{2} +\frac{1}{x^2}=25+2=27$

∴ The correct answer is option (b).

2.

We have,

$x-\frac{1}{x}=5$

Now, squaring both sides, we get

   $(x-\frac{1}{x}) ^{2}=5^{2}$                .......(1)

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

  $x^{2} +\frac{1}{x^2}-2\times x \times\frac{1}{x}=25$

⇒$x^2+\frac{1}{x^2}-2=25$

⇒$x^{2} +\frac{1}{x^2}=25+2=27$       .......(2)

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

$(x^2+\frac{1}{x^2})^2=(27)^2$            .......(3)

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

equation (3), we get

  $(x^2)^2+(\frac{1}{x^2})^2+2\times x^2\times \frac{1}{x^2}=729$

⇒$x^4+\frac{1}{x^4}+2=729$

⇒$x^4+\frac{1}{x^4}=729-2=727$

∴ The correct answer is option (b).