Question

if x-4/(x-2)(x-3)=a/x-2-1/x-3,then find a​

Answer 1

Answer:en the moon is made of green cheese.

Proof: Suppose, for the purpose of contradiction, that the moon is not made of green cheese. Since [math]x+\frac 1 x = 4,[/math] it follows that [math]x[/math] and [math]\frac 1 x[/math] are roots of the quadratic equation in [math]z,[/math]

[math]\qquad z^2–4z+1=0[/math]

The roots of this equation are [math]2+\sqrt 3[/math] and [math]2-\sqrt 3,[/math] which are [math]x[/math] and [math]\frac 1 x[/math] in some order. So [math]x^2+\frac{1}{x^3}[/math] is not [math]12,[/math] but rather either [math]33-11\sqrt3[/math] or [math]33+11\sqrt3,[/math] a contradiction, which completes the proof.

Step-by-step explanation: