Question

If p and q are roots of x^2+2x+1=0 then the values of p^3+q3 becomes

Answer 1

Answer :-

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Given :-

Eqation - x² + 2x + 1 = 0 ------------ ( I )

Roots are - p and q

To find :-

The value of p³ + q³

Salutation :-

Compared the eqation no ( I ) with ax² + bx + c = 0 then we get ,

a = 1

b = 2

c = 1

Now , sum of the roots ( p + q )

= - b / a

= - 2 / 1

= - 2

And , product of roots ( pq )

= c / a

= 1 / 1

= 1

Now , Using identity as we know ,

p³ + q³

= ( p + q )³ - 3pq ( p + q )

= ( - 2 )³ - 3 × 1 × ( - 2 )  [ • Putting the values ]

= - 8 + 6

= - 2               [ ★ Required answer ]

•°• The value of p³ + q³ is - 2.

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Answer 2

x^2+ 2x +1=0

Using factorization method,

x^2 + x + x + 1 = 0

x (x + 1) + 1 (x + 1) = 0

(x + 1) (x + 1) = 0

Hence x + 1 = 0

X = -1 which is p and q.

P^3 + q^3

(-1)^3 + (-1)^3

-1 + (-1)

-1 – 1 = -2