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Manipal MET2015MathematicsTrigonometric Ratios & Identities

If A+ A=m and ^3 A+ ^3 A=n then

Options

  1. Am^3-3 m+n=0
  2. Bn^3-3 n+2 m=0
  3. Cm^3-3 m+2 n=0
  4. Dm^3+3 m+2 n=0

Correct answer

C. m^3-3 m+2 n=0

Step-by-step solution

We have, A+ A=m and ^3 A+ ^3 A=n Now', A+ A=m array ll & ( A+ A)^3=m^3 & ^3 A+ ^3 A+3 A A & & ( A+ A)=m^3 array n+3 A A m=m^3 ...(i) Again, A+ A=m ^2 A+ ^2 A+2 A A=m^2 A A= m^2-1 2 ...(ii) From Eqs. (i) and (ii), we get n+3 m (m^2-1 ) 2 =m^3 array ll & 2 n+3 m^3-3 m=2 m^3 & m^3-3 m+2 n=0 array

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