Answer:
Larger integer is 11.
Step-by-step explanation:
The sum of the squares of two positive integers is 185.
If one integer is 3 less than the other then we have to find the larger integer.
Let the larger integer is x.
Then as per statement of the question smaller integer will be = (x - 3)
Now it has been stated that x² + (x - 3)² = 185
So, x² + x² + 9 - 6x = 185
2x² - 6x + 9 - 185 = 0
2x² - 6x - 176 = 0
x² - 3x - 88 = 0
x² - 11x + 8x - 88 = 0
x(x - 11) + 8(x - 11) = 0
(x + 8)(x - 11)= 0
x = 8, 11
Now we put x = 8 and x = 11 in the given equation Then we find x = 11 is the value that satisfy the equation x²- 3x - 88 = 0
Therefore, the larger integer is 11.
