Algebra

This topic contains 1 reply, has 2 voices, and was last updated by  Ashani Dasgupta 3 months ago.

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  • #21685

    bibhu
    Participant

    solve for a & b?

    #21692

    Ashani Dasgupta
    Keymaster

    Is the question complete?

    For example, if we plug in a = 1, then we will get (possibly complex) solutions of b.

    Computation:

    if a = 1

    \( (1-b)(1 – \sqrt{b} ) = 1 \)

    Expanding we get \( 1 – \sqrt{b} – b + b \sqrt{b} = 1 \)

    This implies \( b \sqrt b = b + \sqrt b \Rightarrow b = \sqrt b + 1 \)

    Set \( \sqrt b =x \) and solve the qudratic.

    This process will work for any value of a.

    This problem reminds me of a problem from Pre RMO 2017. If you expand the given expression you will get \( a \sqrt a + b \sqrt b – a \sqrt b – b \sqrt a = 1 \). The Pre RMO problem set the values of \( a \sqrt a + b \sqrt b = 183 \) and \( a \sqrt b -+ b \sqrt a = 182 \)

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