Question

A meteorite after colliding with a star splinter into two groups of small rocks .the difference between the squares of the number of rocks in each group is 36a times the difference between the number of rocks in each group .how many rocks did the meteorite split into?

Answer 1

Answer:

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Answer 2

Answer:

The number of rocks the meteorite split into is found to be: 36 rocks.

Explanation:

We are given that the meteorite collides into two groups of small rocks,

Let the number of rocks in each of the two groups be 'a' and 'b' respectively,

According to the problem, the difference of squares of 'a' and 'b' is 36 times the difference of 'a' and 'b', thus:

$a^2-b^2=36(a-b)$

Now, we know that the identity of difference of two squares is given be:

$x^2-y^2=(x+y)(x-y)$

Thus, the above expression becomes:

$(a+b)(a-b)=36(a-b)$

Cancelling out $(a-b)$ on both sides, we get:

$a+b=36$

Thus, the total number of rocks, i.e., the sum of number of rocks in each of the two groups, the meteorite divides itself into is found to be 36.

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