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Find the number of ordered triples (x, y, z) of real numbers that satisfy the system of equation : x+y+z=7 ; x^2+y^2+z^2=27 ; x y z=5

Correct answer

03

Step-by-step solution

aligned & x+y+z=7, x^2+y^2+z^2=27, x y z=5 & x y+y z+z x= 49-27 2 =11 aligned Cubic whose roots are x, y, z is t^3-7 t^2+11 t-5=0 Its roots are 1,1,5 (x, y, z) (1,1,5) So number of triplets = 3! 2! =3

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