Solve this: If x2+y2+z2-100xy+yz+zx=-2 and x+y=3z then find the value of z - Maths - Rational Numbers

Question

Solve this:

I f   x 2 + y 2 + z 2 - 100 x y + y z + z x = - 2   a n d
  x + y = 3 z   t h e n   f i n d   t h e
  v a l u e   o f   z

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

x2 + y2 + z2 -100xy + yz + zx = -2x2 + y2 + z2 -100=-2xy - 2yz - 2zxx2 + y2 + z2 +2xy + 2yz + 2zx-100=0x+y+z2 - 100 =03z+z2 -102 = 0                                             Since x+y=3z4z2 - 102 =04z-10 4z+10 =0                                              Since a2-b2=a-ba+b 4z-10=0  or  4z+10=0z=104  or  z=-104z=52  or z=-52 
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Solve this: I f x 2 + y 2 + z 2 - 100 x y + y z + z x = - 2 a n d x + y = 3 z t h e n f i n d t h e v a l u e o f z .

Solve this:

$I f \frac{x^{2} + y^{2} + z^{2} - 100}{x y + y z + z x} = - 2 a n d x + y = 3 z t h e n f i n d t h e v a l u e o f z .$