The sum of the reciprocals of two consecutive even integers is 3/4
Find the two integers.

Let one of those even numbers be x, Then other even number would be x + 2.

According to question,

⇛ Their reciprocal add upto 3/4

So, we can write it as,

⇛ 1/x + 1/x + 2 = 3/4

⇛ x + 2 + x / x(x + 2) = 3/4

⇛ 2x + 2 / x² + 2x = 3/4

Cross multiplying,

⇛ 3(x² + 2x) = 4(2x + 2)

⇛ 3x² + 6x = 8x + 8

⇛ 3x² - 2x - 8 = 0

⇛ 3x² - 6x + 4x - 8 = 0

⇛ 3x(x - 2) + 4(x - 2) = 0

⇛ (3x + 4)(x - 2) = 0

Then, x = -4/3 or 2

☃️ It can't be -4/3 because it is fraction and negative number. So, x = 2

Then, x + 2 = 4

✤ So, The even numbers are 2 and 4.

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step-by-step explanation:

the orientation of the parabolas can easily be found by analysing the power of x and y and their signs. if x is squared , parabola opens up and also if its coefficient is negative it opens down. if y is squared , the parabola opens right and also if its coefficient is negative it opens left. however in order to do the above analysis our equation must be in standard form .

our parabola is

which is not standard form of any parabola . hence we square on both hand side and convert it into standard form.

hence we see that x is squared and its coefficient is non negative . there for it opens up.