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MHT CET20243 May 2024Morning ShiftMathematicsQuadratic EquationActual

The number of roots of the equation, (81)^ ^2 x +(81)^ ^2 x =30 in the interval [0, ] , is equal to

Options

  1. A4
  2. B8
  3. C3
  4. D2

Correct answer

A. 4

Step-by-step solution

aligned & (81)^ ^2 x +(81)^ ^2 x =30 ...(i) & Let y=81^ ^2 x & 81^ ^2 x =81^ (1- ^2 x ) = 81 81^ ^2 x = 81 y aligned Equation (i) becomes aligned & y+ 81 y =30 & y^2-30 y+81=0 & (y-27)(y-3)=0 & y=27 or 3 & 81^ ^2 x =27 or 81^ ^2 x =3 & 3^ 4 ^2 x =3^3 or 3^ 4 ^2 x =3^1 aligned 4 ^2 x=3 or 4 ^2 x=1 x= 3 2 , 1 2 [ x [0, ]] x= 3 , 2 3 , 6 , 5 6 [ x [0, ]] Required number of roots are 4 .

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