Question

Please send me the answer of 25 question ​

Answer 1

$\textbf{\huge{ANSWER:}}$

$\sf{Given:}$

x + y + z = 9

xy + yz + zx = 23

We know by identity That :-

$(x + y + z)^{2} = x^{2} + y^{2} + z^{2} + 2xy + 2yz + 2zx$

Put the given values in it and then solve it :-

=》 $9^{2} = x^{2} + y^{2} + z^{2} + 2 ( xy + yz + zx )$

Solve it further:-

=》 $81 = x^{2} + y^{2} + z^{2} + 2(23)$

Some more steps :-

=》 $x^{2} + y^{2} + z^{2} = 81 - 46$

Subtract and Get the value :-

=》 $x^{2} + y^{2} + z^{2} = 35$

We know by identity that:-

$x^{3} + y^{3} + z^{3} - 3xyz = (x + y + z)(x^{2} + y^{2} + z^{2} - xy - yz - zx)$

Put the obtained values in it and then solve the formed equation further :-

=》 $x^{3} + y^{3} + z^{3} - 3xyz = (9)(35 - ( xy + yz + zx )$

Solve it further now :-

=》 $x^{3} + y^{3} + z^{3} - 3xyz = (9)(35 - 23)$

Subtract and then finally, you will get the answer:-

=》 $x^{3} + y^{3} + z^{3} - 3xyz = 108$

There's your answer!