Question

P+q=12 , pq =27 p3 +q3

Answer 1

Answer:

Step-by-step explanation:

p+q=12

pq=27

(p+q)² = p²+q²+2pq

(12)² = p²+q²+2×27

144 - 54 = p²+q²

90 = p²+q²

Also we have another identity that is

a³+b³=(a+b)(a²+b²-ab)

p³+q³= (p+q)(p²+q²-pq)

= (12)(90-27)

=12×63

=756

Hope it helps you

Answer 2

The value is $p^3+q^3=756$.

Step-by-step explanation:

Given : $p+q=12$ and $pq=27$.

To find : The value of $p^3+q^3$ ?

Solution :

Using algebraic identity, $(a+b)^2=a^2+b^2+2ab$

Here, a=p and b=q

$(p+q)^2=p^2+q^2+2pq$

Substitute the value,

$(12)^2=p^2+q^2+2(27)$

$144=p^2+q^2+54$

$p^2+q^2=90$

Using another algebraic identity, $a^3+b^3=(a+b)(a^2+b^2-ab)$

$p^3+q^3=(p+q)(p^2+q^2-pq)$

Substitute the value,

$p^3+q^3=(12)(90-27)$

$p^3+q^3=(12)(63)$

$p^3+q^3=756$

Therefore, the value is $p^3+q^3=756$.

#Learn more

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