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Re: What is the product of all values of x that satisfies the equation: [#permalink]

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03 Aug 2017, 12:28

I am getting E as my final answer. After squaring both sides, I get x^2-9x+4. The product is 4 which is E in our case. I am confused as to how A is the correct answer? Could anyone please explain it to me?

Re: What is the product of all values of x that satisfies the equation: [#permalink]

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19 Aug 2017, 04:42

As everyone solved, I am getting final equation as \(x^2-9x+4=0\) This gives product of roots as 4 thus E is answer as further solving above equation gives roots which are slighly more than 3/7.

We have \(t_1 = \frac{\sqrt{5}+ \sqrt{13}}{2} \approx 2.9 > 1 > \sqrt{\frac{3}{7}}\). Choose this root. \(t_2 = \frac{\sqrt{5}- \sqrt{13}}{2} \approx -0.7 < 0 < \sqrt{\frac{3}{7}}\). Eliminate this root.

Hence \(x=t_1^2=\frac{9+\sqrt{65}}{2}\).

The answer E.

It's actually x=(9+√65)/2 and x=(9-√65)/2 There are 2 solutions

the best way to check it is b^2-4ac 4 possible scenarios, one of them if the result is positive non-perfect square number then there are 2 irrational solutions but the product of them will be rational number, in that case 4 (9+√65)/2*(9-√65)/2=(81-65)/4=4

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