Question

the difference of the squares of two numbers is 45. the square of the smaller number is 4 times the larger number. determine the numbers.

Answer 1

X^2-Y^2=45
Y^2=4X^2
X=3, Y=6

Answer 2

Numbers are 9 & 6 or 9 & -6

Explanation :

Consider the:

Larger number as x

So,

Square of smaller number = 4x

Square of larger number = x²

Difference of squares of number = 45

Now,

⇒ x² - 4x = 45

⇒ x² - 4x - 45 = 0

Factorisation:

⇒ x² - 9x + 5x - 45 = 0

⇒ x(x - 9) + 5(x - 9) = 0

⇒ (x - 9)(x+ 5) = 0

⇒ x - 9 = 0

⇒ x = 9

&

⇒ x + 5 = 0

⇒ x = -5

Here, The value of x = 9

______________________

Square of smaller number :

→ 4x

→ 4 × 9

→ 36

Smaller number = ± 6

Therefore,

Numbers = 9 & 6 or 9 & - 6

Now,

When,

x = -5

Square of smaller number :

→ 4x

→ 4 × (-5)

→ -20

Hence,

Hence,Numbers are 9 & 6 or 9 & -6