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  • The product of the roots of the equation (x^2-4x+3)^1/2 +(x^2-7x+12)^1/2 =3(x-3)^1/2

The product of the roots of the equation (x^2-4x+3)^1/2 +(x^2-7x+12)^1/2 =3(x-3)^1/2

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Solution:       sqrtx^2-4x+3+sqrtx^2-7x+12=3sqrtx-3

        is defined for  x=3 or xgeq 4 .

       sqrtx-3[sqrtx-1+sqrtx-4]=3sqrtx-3

  Rightarrow   x=3 or    sqrtx-1+sqrtx-4=3

Hence ,  x=3 or x=5

Thus product of roots =15

  h

Posted by

Deependra Verma

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