Question

The differents of squares of two natural numbers is 45. the square of the smaller no. is 4 times the larger number. find the number​

Answer 1

answer is in the picture

Answer 2

$\huge\sf\pink{Answer}$

☞ The numbers are 9 and 6

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$\huge\sf\blue{Given}$

✭ The difference of two squares of 2 numbers is 45

✭ The square of the smaller number is 4 this the larger number

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☆ The Numbers?

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Let the larger number be x and the smaller number be y.

It is given that,

The difference of square of two numbers is 45.

➳ x² - y² = 45 .... (i)

Also, square of smaller number is four times the larger number.

➳ y² = 4x

According to the question ;

x² - y² = 45

➝ x² - 4x = 45 [Since, y² = 4x]

➝ x² - 4x - 45 = 0

On splitting the middle term,

➢ x² - (9 - 5)x - 45 = 0

➢ x² - 9x + 5x - 45 = 0

➢ x(x - 9) + 5(x - 9) = 0

➢ (x - 9)(x + 5) = 0

➢ x = 9 or x = - 5

Thus, by neglecting the negative value

We get the value of x = 9.

Substituting the value of x in (i)

x² - y² = 45

➠ (9)² - y² = 45

➠ 81 - y² = 45

➠ y² = 81 - 45

➠ y² = 36

➠ y = ± √36

➠ y = 6 [Neglecting negative value]

Therefore, the required numbers are-

$\sf\bullet \color{aqua}{\ x = 9}$

$\sf\bullet \color{lime}{\ y = 6}$

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