Question

The difference of the squares of two positive number is 45 . The squares of the smaller number is four times the large number. Find the number

Answer 1

Answer:

Ans: the smaller number = 6

the larger number = 9

Explanation:

Let two no/s be x (greater) and y (smaller)

Then ATQ

 x² - y² = 45          ...(1)

Also, 

y² = 4x          ...(2)

From 1 and 2

Substituting 2 in 1

We get, 

     x² - y² = 45

     x² - 4x = 45

⇒ x² - 4x - 45

⇒ x² - 9x + 5x  -45

⇒ x(x - 9) + 5(x - 9)

⇒ (x+5)(x-9)

⇒ Then x = -5,9

If x = 9

   y² = 4(9)

   y² = 36

    y = √36

    y = 6

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