Question

x2+3x +1=0 then valu of x3+1/x3​

Answer 1

Answer:

-18

Step-by-step explanation:

Given:

⇒x²+3x+1=0,

⇒x²+1=-3x,

⇒x+1/x=-3. --------- 1:)

By cubing both sides,

⇒(x+1/x)³=-27,

⇒x³+(1/x)³+3x×1/x×(x+1/x)=-27,

⇒x³+1/x³+3(x+1/x)=-27,

⇒x³+1/x³+3×-3=-27, From equation 1

⇒x³+1/x³-9=-27,

⇒x³+1/x³=-27+9,

⇒x³+1/x³=-18,

Which is the required answer.

Hope it helps.

Answer 2

Hola,

Let us solve the given equation,

X² + 3x + 1 = 0

let a solve the equation by completing the square root method.

X² + 2*3x*1/2 + 3/2² = 3/2² -1

(X + 3/2)² = 9/4 - 1

= 9-4/4

= 5/4

X+ 3/2 = √5/√4

X = √5/2 - 3/2

X = √5 - 3 /2

so now we have found the value of x now we will put this value of x in the next equation.

X³ + 1/x³

√5 -3/2³ + 1/√5-3/2³

(√5-3)³/8 + 8/(√5-3)³

As we know that,

(a-b)³ = a³ - b³ - 3a²b - 3ab²

Using this formula.

(5√5 - 27 - 45 - 9√5/8) + (8/5√5 - 27 - 45 - 9√5)

(4√5 - 72/8) + (8/4√5 - 72)

-7.881-67.52

-75.401.

I hope my answer I will help you.