Two whole numbers differ by 3. The sum of their squares is 89. what are the numbers?please explain in detail

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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Lets take the two numbers and p and q.

`p-q = 3` -----(1)

`p^2+q^2 = 89` -----(2)

 

from (1)` p = q+3`

`p^2+q^2 = 89`

`(q+3)^2+q^2 = 89`

`q^2+6q+9+q^2 = 89`

`2q^2+6q+9-89 = 0`

`2q^2+6q-80 = 0`

`2(q^2+3q-40) = 0`

`q^2+3q-40 = 0 `

`q^2+8q-5q-40 = 0`

`q(q+8)-5(q+8) = 0`

`(q+8)(q-5) = 0`

`q = -8` or `q = 5`

 

When `q = -8` then `p = -5`

when `q = 5 ` then `p = 8`

 

So the two numbers are (-5,-8) or (8,5)

 

 

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