Question

the difference of the squares of two positive number is 45. the square of the smaller number is four times the larger number. find the numbers

Answer 1

Hey

Here is your answer,

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

Hence x2 = 4y → (1)

Given y2 – x2 = 45

⇒ y2 – 4y = 45
⇒ y2 – 4y – 45 = 0
⇒ y2 – 9y + 5y – 45 = 0
⇒ y(y – 9) + 5(y – 9) = 0
⇒ (y – 9)(y + 5) = 0
⇒ (y – 9)= 0 or (y + 5) = 0

∴ y = 9 or y = -5

But y is natural number, hence y ≠ - 5

Therefore, y = 9

Equation (1) becomes,

x2 = 4(9) = 36
∴ x = 6

Thus the two natural numbers are 6 and 9.

Hope it helps you!

Answer 2

6 & 9 are the no.s . Hope it helps. pls mark brainliest.