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Suppose that there is only one value of x for which the distance from (5,6) to (3x-7,ax+2) is 4. If a≠0 what is a?

 Feb 22, 2021
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$(3x-12)^2+(ax-4)^2=16\implies 9x^2-72x+144+a^2x^2-8ax+16=16\implies (9+a^2)x^2-(72+8a)x+144=0$.

Discriminant is zero, so $(72+8a)^2=4(144)(9+a^2)\implies a=\boxed{\frac{9}{4}}$.

 Feb 23, 2021

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