Question

The difference of the squares of two numbers is
45. The square of the larger number is 4 times
the square of smaller number. Determine the
numbers.​

Answer 1

Answer:

let x and y be the 2 numbers

now

according to your question

see in photo

and if you don't know how to solve quadratic equation then comment on my answer bro!

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Assumption,

Larger number be p

So,

Square of smaller number = 4p

Square of larger number = p²

Difference of squares of number = 45

Situation,

⇒ p² - 4p = 45

⇒ p² - 4p - 45 = 0

Factorize it,

⇒ p² - 9p + 5p - 45 = 0

⇒ p(p - 9) + 5(p - 9) = 0

⇒ (p - 9)(p + 5) = 0

⇒ p - 9 = 0

⇒ p = 9

Or,

⇒ p + 5 = 0

⇒ p = -5

Here,

p = 9

Square of smaller number :-

= 4p

= 4 × 9

= 36

Smaller number = ±6

Hence,

Numbers = 9 & 6 or 9 & - 6

Now,

When,

p = -5

Square of smaller number :-

= 4p

= 4 × (-5)

= -20

Therefore,

Numbers are 9 & 6 or 9 & -6