Question

If a+b=9 and ab=14 what is the value of (a-b)

Answer 1

Answer:

${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ {9}^{2} = {a}^{2} + {b}^{2} + 2(14) \\ 81 = {a}^{2} + {b}^{2} + 28 \\ {a}^{2} + {b}^{2} = 81 - 28 = 53$

${(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab \\ {( a- b)}^{2} = 53 - 2(14) = 53 - 28 = 25 \\ a - b = \sqrt{25} = a - b = 5$