Re: Algebric problem

On 26/06/2024 15:17, Richard Hachel wrote:

One commenter posed the problem:
 sqrt(3x+7)+sqrt(x+2)=1
 On the French forum, mathematicians had some problems with this.
 However, the solution is very simple, and requires three lines of calculations on a piece of paper.
 R.H.

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Square both sides + rearrange giving
    ..linear fn of x.. = sqrt(..quadratic fn of x..)
Square both sides giving
    ..quadratic fn of x.. = ..another quadratic fn of x..
Solve quadratic giving 2 possibilities for x.
Check back with original equation (since squaring may introduce extra solutions)
My working gives the quadratic x^2+3x+2 = 0  solutions x = -1 or x = -2.
Checking with original equation:  x=-1 fails.  x=-2 works, so only solution is x=-2.
Mike.