Math, asked by sia42, 1 month ago

If x =4-root 15 find the value of x^2 + 1/x^2

Answers

Answered by BangtanGirl11
3

Answer:

x² + 1/x² = 62

If x is equal to 4 root 15, how would one find the value of x squared plus 1 by x squared?

Did you mean, 4 + root (15)? :D

If yes, then, instead of squaring it completely, and then rationalizing it, which takes a lot of your time might not be the way to go.

(x^2)+ 1/(x^2) can be written as

= ( x + 1/x)^2 - 2

x = 4 + root(15), right?

You know what the best part is? Figuring out 1/x. And this is how I'm guessing you may have posed your question wrongly.

1/x = 1/( 4 + root(15) ), right? Now rationalize this, by multiplying 4 - root(15), in ths numerator and the denominator, so basically we are multiplying 1. Right? So far, so good.

The numerator has 4 - root(15), and our denominator has the product

(4 + root(15)) * (4 - root(15)),

Which is of the format,

(a + b) * (a - b) = a^2 - b^2

Hence our product becomes,

= 4^2 - (root (15))^2 = 1.

Voila our question has become easier, and this is how I guessed your question was posed as such.

Hence 1/x = 4 - root(15)

Now calculating the value of,

x + 1/x = 4 + root(15) + 4 - root(15) = 8

And,

(x + 1/x)^2 - 2 = (8)^2 - 2 = 62. Which is our answer.

But if you did mean, 4 times root(15) but not 4 + root(15), then I apologize,

In that case,

x^2 = (4*root(15))^2 = 16*15 = 240. And our desired answer is,

x^2 + 1/(x^2)

= 240 + ( 1/240 ) = (57601)/240. For exact values, please refer to a calculator

Answered by Anonymous
1

Answer:

the above one is the right answer of your question please mark as brainlist answer to above

Similar questions