solve the java expression x³+XYZ+Y³
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Answer:
Given :-
→ x + y + z = 15.
→ xy + yz + zx = 71.
→ xyz = 10.
➡ To find :-
→ x³ + y³ + z³ .
▶ Solution :-
Here
x + y + z = 15.
=> ( x + y + z )² = ( 15 )² .
=> x² + y² + z² +2 xy + yz + zx = 225.
=> x² + y² + z² + 2 × 71 = 225.
=> x² + y² + z² + 142 = 225.
=> x² + y² + z² = 225 - 142.
•°• x² + y²+ z² = 83.
Now Here
→ x³ + y³ + z³ - 3xyz = ( x + y + z )( x² + y² + z² - ( xy + yz + zx ) .
=> x³ + y³ + z³ - 3( 10 ) = ( 15 )( 83 - ( 71 ) ).
=> x³ + y³ + z³ - 30 = 15 × ( 83 - 71 ) .
=> x³ + y³ + z³ - 30 = 15 × 12.
=> x³ + y³ + z³ = 180 + 30 .
•°• x³ + y³ + z³ = 210.
Hope this helps you to gain Knowledge in Sums
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