infinite solutions.

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Joined: Aug 4, 2011

by hemangsarkar, Sep 13, 2012, 5:23 AM

Q) show that $\sqrt{x+3-4\sqrt{x-1}} + \sqrt{x+8-6\sqrt{x-1}} = 1$

has infinitely many real solutions.

solution : $x - 1 = t^2$

plugging it back into the equation, we get

$|t-2| + |t-3| = 1$

we can see that for $2 \geq t \geq 3$ , this is true.

hence any value of $x$ in $[5,10]$ satisfies this.