if x = 5-2root 6 find the value of x square - 1/x square
answers pleas
Note that if
x = 5-2√6
1/x = 5+2√6
Now just crank it out
To find the value of x² - 1/x², we need to first calculate the value of x.
Given: x = 5 - 2√6
Let's simplify this expression.
We know that a - √b can be simplified as a - b√c, where:
a = the constant term
b = coefficient of the square root term
c = the term inside the square root
In our given expression, we have:
a = 5
b = 2
c = 6
Therefore, x = 5 - 2√6 can be simplified as:
x = 5 - 2 * √6
= 5 - 2 * (√2 * √3) [since √6 = √2 * √3]
= 5 - 2√2√3
= 5 - 2√2(√3)
= 5 - 2√2√3
= 5 - 2√(2 * 3)
= 5 - 2√(6)
= 5 - 2 * (√6)
= 5 - 2 * (√6)
= 5 - 2(2.449)
= 5 - 4.899
= 0.101
Now, let's find the value of x² - 1/x².
x² = (0.101)²
= 0.010201
To find 1/x², we need to take the reciprocal of x².
1/x² = 1/0.010201
= 98.0272
Now, let's compute x² - 1/x².
x² - 1/x² = 0.010201 - 98.0272
= -98.016
Therefore, x² - 1/x² is approximately equal to -98.016.