Question

Q. If p+q+r=6 and pq + qr + rp=5 , then find the value of p³ + q³+ r³- 3pqr.




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Answer 1

Given:-)

→ p + q + r = 6.

→ pq + qr + rp = 5.

To Find :-)

→ p³ + q³ + r³ - 3pqr.

▶ We have,

=> p + q + r = 6.

[ Squaring both side ]

=> ( p + q + r ) ² = 6².

=> p² + q² + r² + 2 ( pq + qr + rp ) = 36.

=> p² + q² + r² + 2 ( 5 ) = 36.

=> p² + q² + r² + 10 = 36.

=> p² + q² + r² = 36 - 10.

=> p² + q² + r² = 26.

▶Now,

=> p³ + q³ + r³ - 3pqr = ( p + q + r ) ( p² + q² + r² - ( pq + qr + rp ) ).

= ( 6 ) ( 26 - (5) ).

= 6 × 21.

= 126.

✔✔Hence, it is solved ✅✅.

Answer 2

Answer:

126

Step-by-step explanation:

p+q+r=6

squaring

(p+q+r)²=36

p²+q²+r²+2pq+2qr+2pr=36

p²+q²+r²+2*(pq + qr + rp)=36

p²+q²+r²+2*5=36

p²+q²+r²=26-------------------------(1)

===============================================

Now p³ + q³+ r³- 3pqr.=(p+q+r)(p²+q²+r²-pq-qr-pr)

=(6)[ 26-5)

=6*21

=126