- - - If a = 2, b = 3, c = 1, d = 0, find the numerical value.
7. 3abc 2bcd + 2cda - 4dab. 8. 2bc + 3cd 4da + 5ab 9. 3bcd + 5cda – 7dab + abc. 10. a2 + b2 + 2 + d? 11. 2q2 + 363 – 464. 12. a* + 64 - c. - -
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Question
If a+b+c=9 and a
2
+b
2
+c
2
=35, then find the value of a
3
+b
3
+c
3
−3abc
Medium
Solution
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Correct option is B)
a+b+c=9 and a
2
+b
2
+c
2
=35
Using formula,
(a+b+c)
2
=a
2
+b
2
+c
2
+2(ab+bc+ca)
9
2
=35+2(ab+bc+ca)
2(ab+bc+ca)=81−35=46
(ab+bc+ca)=23
using formula,
(a
3
+b
3
+c
3
)−3abc=(a
2
+b
2
+c
2
−ab−bc−ca)(a+b+c)
a
3
+b
3
+c
3
−3abc=(35−23)×9=9×12=108
Answer (B) 108
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