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Alex Ar [27]
3 years ago
11

David did not notice the multiplication sign between two three-digit numbers and wrote one six-digit number, which is equal to s

even times their product. Find these numbers.
Also:

Let's call three prime numbers "cool" if their product is five times greater than their sum. How many "cool" triples are there?
Mathematics
1 answer:
IRISSAK [1]3 years ago
4 0

1) We can get that number hit and trial method.

It is said that "two three-digit numbers and wrote one six-digit number, which is equal to seven times their product".

Let us check number 143.

If we write 143 two times without any sign in between , we get 143143 ( a six digit number).

But if we multiply 143 × 143 , we get 20449.

7 times of 20449 equals 143143.

<h3>Therefore, the required three digit number is 143.</h3>

2) Let us assume required prime numbers are a, b and c.

Product of a, b and c= abc.

Sum of a, b and c = a+b+c.

"Their product is five times greater than their sum."

Therefore,

abc = 5(a+b+c)  ----------------------equation (1)

Now, let us take first prime numbers 2 and second 5.

Plugging a=2 and b=5.

2×5×c = 5(2+5+c).

10c = 5(7+c)

10c = 35 +5c.

Subtracting 5c from both sides, we get

10c-5c = 35 +5c-5c.

5c = 35.

Dividing both sides by 5, we get

c=7.

Therefore, first "cool" triple is 2,5,7.

Let us check by taking a=2 and b=7.

Plugging a=2 and b=7 in equation (1), we get

2×7×c = 9(2+7+c).

c=9. But it's not a prime number.

Let us take a=2 and b=11, we get

2×11×c = 11(2+11+c).

c=13   (A prime)

If we take a=2 and b=17, we get

2×17×c = 17(2+17+c).

c=19   (A prime).

<h3>On the same way, if we continue the process, we can get many "cool" triples.</h3>


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