If x²+ 1/x²=32 then the value of X-1/x is?
Answers
Step-by-step explanation:
If x^2 + 1/(x^2) = 23, find x?
Let x^2 + 1/(x^2) = 23 be >>> Equation (1)
It would be helpful if we could find an expression which gave us all or part of Equation (1).
Let us consider
( x + 1/x )^2 >>> Equation (2)
Expanding Equation (2) we get:
x^2 + 2 + 1/( x )^2 >>>>> Equation (3)
Therefore re-arranging Equation(3)
[( x^2 + 1/(x)^2)] + 2 is the same as 23 + 2 = 25.
That is [ x^2 + 1/( x )^2 ] = 25 >>>>>> Equation (4)
Now take the square root of both sides of Equation (4).
[ x + 1/x ] = sqrt ( 25 ) or
(x + 1/x) = (+\-) 5 >> Equation (5)
Let us reformat Equation (5) by multiplying every term by x.
[ x^2 + 1 ] = (+\-)(5x) >>> Equation (6)
Re-arranging Equation (6)
x^2 (+\-)5x + 1= 0 >>>> Equation (7)
Case (1) +5x
Roots = [ -5 (-\+) sqrt (25 - 4) ]/2 or
Roots are: -4.7913 and -0.20871
Case (2) -5x
Roots = [ +5 (-\+)sqrt (25 - 4) ]/2 or
Roots are +4.7913 and +0.20871
It would have been nice to find the roots were nice clean integers. But apparently not!
So to check, I graphed the original equation as below and confirmed that the analysis was correct.
