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kodGreya [7K]
3 years ago
13

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

Mathematics
2 answers:
GenaCL600 [577]3 years ago
8 0

Answer:

1 - 27 , 2- 727

Step-by-step explanation:

see image for explanation

vredina [299]3 years ago
5 0

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).

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