Find the value of 30³+20³-50³ without any calculation of cube
Answers
Answered by
5
Answer:
30
3
+20
3
−50
3
=−90000
Step-by-step explanation:
I have used the following formula to find the value of the given expression.
Formula used:
If\:x+y+z=0,\:then\:x^3+y^3+z^3=3xyzIfx+y+z=0,thenx
3
+y
3
+z
3
=3xyz
Given:
30^3+20^3-50^330
3
+20
3
−50
3
30^3+20^3+(-50)^330
3
+20
3
+(−50)
3
x^3+y^3+z^3x
3
+y
3
+z
3
where x=30, y=20, z=-50
Also,
x+y+z=30+20+(-50)=0x+y+z=30+20+(−50)=0
Using the above formula
x^3+y^3+z^3=3xyzx
3
+y
3
+z
3
=3xyz
30^3+20^3+(-50)^3=3(30)(20)(-50)30
3
+20
3
+(−50)
3
=3(30)(20)(−50)
30^3+20^3+(-50)^3=(1800)(-50)30
3
+20
3
+(−50)
3
=(1800)(−50)
30^3+20^3+(-50)^3=-9000030
3
+20
3
+(−50)
3
=−90000
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