Let \(\displaystyle{x}_{{{1}}}\ \text{and}\ {x}_{{{2}}}\) be the real

talpajocotefnf3

talpajocotefnf3

Answered question

2022-03-23

Let x1 and x2 be the real root of the equation x2kx+(k2+7k+15)=0, if the maximum value of (x12+x22)=d18x, then find the value of x?

Answer & Explanation

exinnaemekswr1k

exinnaemekswr1k

Beginner2022-03-24Added 10 answers

First, it seems like you're using the symbol x to denote 2 different things (the variable in the quadratic equation, and the number we need in 18x). Avoid doing that because it causes confusion.
Next, the problem with your solution is that you have a condition on k. The discriminant D=3k228k60 has to be non-negative for the quadratic to have real roots. Solving D0 gives k[6,103]. So, you have to find the maximum of f(k)=k214k30 on [6,103]. Instead, you found the maximum over R which is obtained when k=7, and that's not in the interval. That's why you got a wrong answer. You'll find that f is decreasing in [6,103], so the maximum is f(6)=18, and the answer follows.

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