Question

If a - b = 7 and ab = 18; find a + b.

Answer 1

We know that,
( a - b )² = a² - 2ab + b²
and
( a + b )² = a² + 2ab + b²
Rewrite the above equation, we have
( a + b )² = a²  + b² - 2ab + 4ab
               = ( a + b )² + 4ab              ...(1)
Given that a - b = 7; ab = 18
Substitute the values of ( a - b ) and (ab)
in equation (1), we have
( a + b )² = (7)² + 4(18)
              = 49 + 72 = 121
⇒ a + b = `+- sqrt121`
⇒ a + b = `+-11`