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