the difference of the squares of two natural numbers is 45.the square of the smaller number is four times the larger number.find the numbers
Answers
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.
Answer:
9,6
Step-by-step explanation:
let a,b be the two natural no.s
=> a² - b² = 45 and ------------------------- 1
b² = 4a , -------------------------------------------- 2
find a,b ?
substitute 2 in 1 =>
a² - 4a = 45
a²-4a-45 = 0
on factorising , we get (a-9)(a+5) =0
so, either a-9 = 0 => a=9
or a+5 = 0 => a=-5
eliminate a=-5 as square of a no. cannot be negative.(see 2 )
so a = 9
and by 2, b² = 4*9
=> b² = 36
=> b = 6