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What is the integer solution of #6x^2+9=21x#?

Answer 1

Re-arrange #6x^2+9 = 21x# into the more usual form #6x^2-21x+9 = 0#

then factor the left hand side #(6x-3)(x-3)=0#

which implies either #(6x-3)=0# ...but this does not have an integer solution or #(x-3) = 0# ...which has an integer solution #x=3#

The only integer solution to #6x^2+9=21x# is #x=3#

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Answer 2

Julia Adams

To find the integer solutions of the equation 6x^2 + 9 = 21x, we first rewrite it in standard form:

6x^2 - 21x + 9 = 0

Next, we factor out the greatest common factor, which is 3:

3(2x^2 - 7x + 3) = 0

Now, we need to factor the quadratic expression inside the parentheses:

2x^2 - 7x + 3 = (2x - 1)(x - 3)

Setting each factor to zero gives us the possible values for x:

2x - 1 = 0 => 2x = 1 => x = 1/2 x - 3 = 0 => x = 3

However, we are looking for integer solutions, so the only integer solution is x = 3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.