Question

x+y+z=9and xy+yz+zx=26 to x²+ y²+z²= ?

Answer 1

Heya..........!!!

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This question can be easily solved by applying the identity :

=> ( x + y + z )² = x² + y² + z² + 2 ( xy + yz + zx )


Given in the question :

--» x + y + z = 9
--» xy + yz + zx = 26


=> ( 9 )² = x² + y² + z² + 2 ( 26 )

=> 81 = x² + y² + z² + 52

=> x² + y² + z² = 81 - 52



♦ 29. is the required answer .



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Hope It Helps You ☺

Answer 2

Given x+y+z = 9
xy + yz + zx = 26

[We know that (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca]

Now Take

x + y + z = 9

squaring on both sides

(x + y + z)^2. = (9)^2

x^2 + y^2 + z^2 + 2xy + 2yz + 2zx = 81

x^2 + y^2 + z^2 + 2(xy + yz + zx) =81

x^2 + y^2 + z^2 + 2(26) = 81

x^2 + y^2 + z^2 +52 = 81

x^2 + y^2 + z^2 = 81 - 52

x^2 + y^2 + z^2 = 29....is the required answer..