Respuesta :
Answer:
Smallest consecutive number = 6
Second consecutive number = 8
Largest consecutive number = 10
Step-by-step explanation:
Let us assume the first even number = k
Then the next consecutive even number (k +2)
And the third consecutive even number = (k+2) + 2= k + 4
Now, Product of two smaller number = k (k+2)
Also, the square of the largest number = [tex](k+4)^2[/tex]
Now, according to the question:
[tex]k(k+2) = (k+4)^2 - 52[/tex]
Now, using ALGEBRAIC IDENTITY: [tex](a+b)^2 = a^2 + b^2 + 2ab[/tex]
[tex]k(k+2) = (k+4)^2 - 52 \implies k ^2 + 2k = k^2 + 8k + 16 -52\\or, 2k - 8k = 16 - 52 \implies -6k = -36\\\implies k = 36/6= 6[/tex]
or, k = 6
Hence, the smallest consecutive number = k = 6
Second consecutive number = k + 2 = 6 + 2 = 8
Largest consecutive number = k + 4 = 6 + 4 = 10
Hence, 6 , 8 and 10 are the required numbers.
