Question

If square of a natural number diminished by 75 is equal to 10 times of that number, then the number is​

Answer 1

Given :- If square of a natural number diminished by 75 is equal to 10 times of that number, then the number is ?

Solution :-

Let us assume that, the given number is x .

so,

→ square of x - 75 = 10 times of x

→ x² - 75 = 10x

→ x² - 10x - 75 = 0

splitting the middle term ,

→ x² - 15x + 5x - 75 = 0

→ x(x - 15) + 5(x - 15) = 0

→ (x - 15)(x + 5) = 0

putting both equal to zero we get,

→ x = 15 and (-5) .

since x is a natural number it cant be negative.

Hence, the required number is 15 .

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Answer 2

Given : square of a natural number diminished by 75 is equal to 10 times of that number,

To Find : the number is​

Solution:

Let say natural number = n

square of a natural number = n²

diminished by 75  = n² - 75

10 times of that number, =  10n

Equate both

=>   n² - 75 = 10n

=> n² - 10n - 75 = 0

=> n² - 15n + 5n - 75 = 0

=> (n - 15)(n + 5)  = 0

=> n = 15 , n  =  - 5

n is a natural number hence must be a +ve integer  so  n can not be - 5

so n = 15

Verification :

15² = 225

225 - 75 = 150

15 * 10  = 150

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