Question

If a +b =7 and ab = 10 find a-b

Answer 1

`\sf \: a + b = 7 => a=7-b- - - - (1) \\ \sf \: ab = 10 - - - --(2)`

Put equation 1 in 2:

`\sf(7 - b) b= 10`

`\sf7b - {b}^(2) = 10`

`\sf { - b}^(2) + 7b - 10 \\ \sf {b}^(2) - 7b + 10`

Factor the quadratic equation:

`\tt {b}^(2) - 7b + 10 \\ \tt {b}^(2) - 5b - 2b + 10 \\ \tt \: b(b - 5) - 2(b - 5) \\ \tt \: (b - 5)(b - 2) \\ \tt \: b_(1) = a = 5 \: and \: b_(2) = 2`

Therefore,

• a = 5
• b = 2

Answer 2

Answer: a-b = 3

Step-by-step explanation: if the a = 5 and the b = 2 a+b=7 ab=10