Question

The difference between positive number is 7 and the square of their sum is 289. Find the two numbers

Answer 1

Answer:

5 and 12

Step-by-step explanation:

Let the numbers be n and (n + 7)   [∵ difference is 7]

According to question

( n + n + 7)² = 289

(2n + 7)² = 289

4n² + 28n + 49 = 289

4n² + 28n - 240 = 0

Dividing whole equation by 4

n² + 7n - 60 = 0

Splitting middle term

n² + 12n - 5n - 60 = 0                     [∵ (12 - 5) = 7 and 12 × ( -5) = -60]

taking n common from first two terms and -5 from last two terms

n ( n + 12) -5( n + 12) = 0

(n + 12) (n - 5) = 0

n + 12  = 0                        n - 5 = 0

n = -12                              n = 5

it is given that numbers are positive, ∴ neglecting n = -12

∴ Desired numbers are 5 and 12   [n  = 5, n + 7 = 12]