Question

x⁴+1/x⁴=194 , find the value of x²+1/x² and x+1/x

Answer 1

Step-by-step explanation:

Given : x⁴ + 1/x⁴ = 194

To find : value of x³ + 1/x³,x² + 1/x²,+and , x + 1/x

Solution :

We know that

(x² + 1/x² )² = (x²)² + (1/x²)² + 2 x² × 1/x²

(x² + 1/x² )² = x⁴ + 1/x⁴ + 2

(x² + 1/x² )² = 194 + 2

(x² + 1/x² )² = 196

(x² + 1/x² )² = 14²

x² + 1/x² = 14……….(1)

[Taking square root of both sides]

Now ,

we know that (x + 1/x)² = x² + 1/x² + 2

(x + 1/x)² = 14 + 2

[From eq 1]

(x + 1/x)² = 16

(x + 1/x)² = 4²

x + 1/x = 4 ………..(2)

On Cubing eq 2 both sides :

(x + 1/x)³ = 4³ ...........(3)

By Using Identity : (a + b)³ = a³ + b³ + 3ab(a + b)

(x)³ + (1/x)³ + 3 × x× 1/x (x + 1/x) = 64

x³ + 1/x³ - 3(x + 1/x) = 64

x³ + 1/x³ + 3(4) = 64

[From eq 3}

x³ + 1/x³ + 12 = 64

x³ + 1/x³ = 64 -12

x³ + 1/x³ = 52

Hence the value of the value of x³ + 1/x³ is 52 , x² + 1/x² is 14 and x + 1/x is 4.

HOPE THIS ANSWER WILL HELP YOU

Answer 2

Answer:

The sum of father's present age and son's present age=100yrs.If we half the age of father and add to present age of son we get 65yrs.Find the present age of father and son.