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AP EAMCET20228 Jul 2022Evening ShiftMathematicsQuadratic EquationActual

If y^2+z^2=a y z, z^2+x^2=b x z, x^2+y^2=c x y , then the value of x z y^2 + y^2 z x is

Options

  1. Aa^2-b^2+c^2
  2. Ba^2+b^2+c^2
  3. Ca c-b
  4. Da b-c

Correct answer

C. a c-b

Step-by-step solution

y^2+z^2=a y z y^2+z^2 y z = a y z y z y z + z y =a ...(i) z^2+x^2=b z x z x + x z =b ...(ii) and x^2+y^2=c x y x y + y x =c ...(iii) Multiplying Eqs. (i) and (iii), ( y z + z y ) ( x y + y x )=a c x z + y^2 z x + z x y^2 + z x =a c ...(iv) On subtracting Eq. (ii) from Eq. (iv), ( x z + z x + y^2 z x + z x y^2 )- ( z x + x z )=a c-b y^2 z x + z x y^2 =a c-b

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