Question

The roots of X+(1/X)=5/2 are

Answer 1

GIVEN :

$x+ \frac{1}{x} = \frac{5}{2}$

TO FIND :

$roots \: of \: \: = > x+ \frac{1}{x} = \frac{5}{2}$

FORMULA USED:

Roots = (-b ± √D)2a

where D => discriminant = b²-4ac

a = coefficient of x²

b = coefficient of b

c = constant term

SOLUTION :

$⟹x+ \frac{1}{x} = \frac{5}{2}$

⟹ LCM of 1 and x = x

$⟹ \frac{ {x}^{2} + 1}{x} = \frac{5}{2}$

now cross multiply :-

$⟹ ({x}^{2} + 1) \times 2= 5 \times x$

$⟹2 {x}^{2} + 2 = 5x$

$⟹2 {x}^{2} - 5x+ 2 = 0$

Therefore , D ( discriminant) = b²-4ac

In the given equation ⟶ 2x²-5x+2=0

a = 2

b = -5

c= 2

=>( 5)²-(4×2×2)

=> 25-16

=> 9

Roots = (-b ± √D)2a

we have took out the value of D = 9

therefore , √D = √9 = ± 3

Roots =[ -(-5) ± 3]/(2×2)

⟹ 5± 3/4

⟹ 5+3/4 or 5- 3/4

⟹ 23/4 or 17/4

ANSWER :

Roots = 23/4 and 17/4