Question

if th sum of square of two positive integer is 117. if square of smaller number is 4 times of larger number. then find the positive integer​

Answer 1

Answer:

6 and 9

Step-by-step explanation:

Let the two numbers be x and y

According to the question,

x² + y² = 117   ...   (i)

Also,

x² = 4y   ...   (ii)

Use, (ii) in (i)

4y + y² = 117

y² + 4y - 117 = 0   ...   (iii)

Factors of 117 are 1 x 117, 3 x 39 and 9 x 13

13 - 9 = 4

so, 4y can be written as 13y - 9y

Rewriting (iii),

y² + 13y - 9y - 117 = 0

y (y + 13) - 9 (y + 13) = 0

(y - 9) (y + 13) = 0

y - 9 = 0 or y + 13 = 0

y = 9 or y = -13

As -13 is a negative integer, it is not possible.

So, y = 9

Using y = 9 in (ii)

x² = 4 * 9 = 36

x = √36

x = 6

So, the two positive integers are 6 and 9.