Question

11. Find two consecutive positive even integers whose product is 288.​

Answer 1

Answer:

Now here,we consider the even integers to be x and the other as it is even and consecutive to be x+2.

so, According to the question,

x(x+2)=288

so,x²+2x-288=0

On solving the quadratic equation we get x=16 and -18.

Since it should be positive number x=16 and so the other number is 18.

Step-by-step explanation:

If you multiply 16 and 18 you get 288.

Answer 2

$\huge\star{\green{\underline{\mathfrak{Answer :-}}}}$

16 and 18.

$\huge\star{\green{\underline{\mathfrak{Explanation :-}}}}$

Let the two consecutive positive integers be : x and x+2.

It is given that their product is equal to 288.

Therefore,

$\leadsto {(x + 2) = 288}$

$\leadsto { {x}^{2} + 2x = 288}$

$\leadsto { {x}^{2} + 2x - 288 = 0}$

By splitting the middle term,

$\leadsto { {x}^{2} + 18x - 16x - 288 = 0}$

$\leadsto {(x + 18) - 16(x + 18) = 0}$

$\leadsto {(x - 16)(x + 18) = 0}$

$\leadsto { (16) \: and \: ( - 18)}$

Therefore, the numbers are : 16 and 18(neglecting the negative sign).

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