Question

1
1
If x2 +
23, evaluate: (i) x +
(ii) x
х
X
x
2 1.2​

Answer 1

Answer:

If x^2 + 1/(x^2) = 23, find x

Let x^2 + 1/(x^2) = 23 be >>> Equation (1)

( x + 1/x )^2 >>> Equation (2)

When we Expanding Equation (2) we get:

x^2 + 2 + 1/( x )^2 >>>>> Equation (3)

[ x^2 + 1/( x )^2 ] = 25 >>>>>> Equation (4)

x + 1/x) = (+\-) 5 >> Equation (5)

[ x^2 + 1 ] = (+\-)(5x) >>> Equation (6)

x^2 (+\-)5x + 1= 0 >>>> Equation (7)

Case (1) +5x

Roots = [ -5 (-\+) sqrt (25 - 4) ]/2

X=10.5