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Manipal MET2019MathematicsTrigonometric Equations

The equation 3 x+4 x=6 has ..... solution.

Options

  1. Afinite
  2. Binfinite
  3. Cone
  4. Dno

Correct answer

D. no

Step-by-step solution

Given that 3 x+4 x=6 Since the maximum value of (3 x+4 x)=+ 3^2+4^2 =5 . Hence there is no ' x ' satisfying 3 x+4 x=6 . No solution, as | x| 1,| x| 1 and both of them do not attain their maximum value for the same angle. Alternate Method, 3 x+4 x=6 Let r =3 and r =4 array lr & = ⁻¹ ( 4 3 ) & 5( x+ x)=6 array ( -x)= 6 5 or (x- )= 6 5 or (x- ) 1 but -1 x 1 . There exist no solution in [-1,1] .

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