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

LET THE TWO NUMBERS BE X AND Y

X^2 + Y^2 = 45

Y^2 = 4X

X^2+4X = 45

ON FACTORIZING

(X - 9) (X + 5) ARE THE FACTORS

SO X =9,-5

HENCE X IS NOT NEGATIVE SO

X = 9

WHEN X =9

X^2 = 9*4

X =6
THEN THE NUMBERS ARE 6 AND 9

Answer 2

Answer:

Hence, the numbers are (9, 6) or (9, -6).

Step-by-step explanation:

Given :

• Difference of the squares of two numbers is 45.
• The square of the smaller number is 4 times the large number.

To find :-

The numbers.

Solution :

Let the larger number be x, then the square of smaller number will be 4x and square of larger number as x². Difference of squares of number is 45.

ATP :

⇛ x² - 4x = 45

⇛ x² - 4x - 45 = 0

➛ (9 × 5 = 45) & (-9 + 5 = -4)

⇛ x² - 9x + 5x - 45 = 0

⇛ (x - 9)(x+ 5) = 0

⇛ x = 9 or x = -5

✮ Square of smaller number :

• 4x
• 4(9)
• 36

↦ Smaller number is ±6.

↦ Numbers are (9, 6) or (9, -6)

✮ Square of smaller number :

• 4x
• 4(-5)
• -20

Hence, the numbers are (9, 6) or (9, -6).