Question

Find the integers of the word problem stated above​

Answer 1

Question:

The sum of squares of two consecutive positive integers is 145. Find the integers.

Solution:

Let the two consecutive integers be x and (x+1)

Now, it is said that sum of squares of two consecutive positive integers is 145 i.e.

x² + (x+1)² = 145

x² + x² + 2x + 1  = 145

2x² + 2x + 1 = 145

2x² + 2x + 1 - 145 = 0

2x² + 2x - 144 = 0

x² + x - 72 = 0

A quadratic equation is formed let's find out it's roots by splitting the middle term

x² - 8x + 9x - 72 = 0

x(x - 8) + 9(x - 8) = 0

(x - 8)(x + 9) = 0

The two roots are

x - 8 = 0 => x = 8

x + 9 = 0 => x = -9

The two consecutive integers can be found,

when x = 8,

First integer, x = 8

Second integer, x + 1 => 8 + 1 = 9

when x = -9

First integer, x = -9

Second integer, x + 1 => -9 + 1 = -8

But, it is said in question two consecutive positive integers.

The two consecutive positive integers are 8 and 9.

Answer 2

Answer:

-1 is word problem started