Without actually calculating cubes,find the value of (15)³+(-9)³+(-6)³
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Answered by
2
Answer:
(i) (-12)³ + (7)³+ (5)³
Let x = -12, y = 7 & z = 5
x + y + z = -12 + 7 + 5 = 0
Here, x + y + z = 0
We know that if,
x + y + z = 0, then x³ + y³ + z³ = 3xyz
(-12)³ + (7)³ + (5)³ = 3(-12)(7)(5) = -1260
(-12)³+ (7)³+ (5)³ = - 1260
(ii) (28)³ + (–15)³ + (-13)³
Let x = 28, y = -15 and z = -13
x + y + z = 28– 15 – 13 = 0
Here, x + y + z = 0
We know that if, x + y + z = 0,
then x³ + y³ + z³ = 3xyz
(28)³+ (–15)³ + (-13)³ = 3(28)(-15)(-13) = 16380
(28)³+ (–15)³ + (-13)³ = 16380
Answered by
4
Answer :
(15)³ + (-9)³ + (-6)³
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Take cube as common :
[ 15 + (-9) + (-6)]³
=> (15 - 9 - 6)³
=> (15 - 15)³
=> 0³
= 0
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